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- 02:52, 15 August 2018 Polar Form of Complex Number/Examples (hist) [283 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Polar Form of Complex Number == <onlyinclude> === Example: $i$ === {{:Po...")
- 02:05, 15 August 2018 Argument of Complex Conjugate equals Argument of Reciprocal (hist) [1,572 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $z \in \C$ be a complex number. Then: :$\arg {\overline z} = \arg \dfrac 1 z = -\arg z$ where: :$\arg$ denotes the Definit...")
- 01:50, 15 August 2018 Polar Form of Reciprocal of Complex Number (hist) [1,285 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $z := r \left({\cos \theta + i \sin \theta}\right) \in \C$ be a complex number expressed in polar form. Then:...")
- 17:02, 14 August 2018 Complex Modulus of Product of Complex Numbers/Proof 3 (hist) [1,174 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Complex Modulus of Product of Complex Numbers}} == Proof == <onlyinclude> Let: : $z_1 = r_1 \left({\cos \theta_1 + i \sin \theta_1}\right)$ : $z_2 = r_2 \lef...")
- 16:48, 14 August 2018 Argument of Complex Number/Examples/-i (hist) [1,389 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg \left({-i}\right) = -\dfrac \pi 2$ </onlyinclude> == Proof == We h...")
- 16:44, 14 August 2018 Argument of Complex Number/Examples/2i (hist) [1,380 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg \left({2 i}\right) = \dfrac \pi 2$ </onlyinclude> == Proof == We h...")
- 04:27, 14 August 2018 Argument of Complex Number/Examples/-1-i/Mistake (hist) [681 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Complex Numbers|1960|Walter Ledermann}}: : Chapter $2$: Geometrical Representations :: Example $\text{(iv)}$ This mistake can be seen in th...")
- 03:18, 14 August 2018 Argument of Complex Number/Examples/-1-i (hist) [1,464 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg \left({-1 - i}\right) = -\dfrac {3 \pi} 4$ </onlyinclude> == Proof...")
- 02:11, 14 August 2018 Argument of Complex Number/Examples/1+i (hist) [1,382 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg \left({1 + i}\right) = \dfrac \pi 4$ </onlyinclude> == Proof == We...")
- 02:11, 14 August 2018 Argument of Complex Number/Examples/-3 (hist) [1,332 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg \left({-3}\right) = \pi$ </onlyinclude> == Proof == We have that:...")
- 01:19, 14 August 2018 Argument of Complex Number/Examples/3 (hist) [1,277 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Argument of Complex Number == <onlyinclude> :$\arg 3 = 0$ </onlyinclude> == Proof == We have that: :$3 = 3 + 0 i$ an...")
- 17:40, 13 August 2018 Argument of Complex Number/Examples (hist) [944 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Argument of Complex Number == <onlyinclude> === Example: $\arg 3$ === {{:Arg...")
- 17:10, 13 August 2018 Conversion between Cartesian and Polar Coordinates in Plane (hist) [1,684 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be the plane. Let a cartesian plane $C$ be applied to $S$. Let a Definition:Polar Coordinate...")
- 02:34, 13 August 2018 Equation of Line in Complex Plane/Formulation 2 (hist) [1,692 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\C$ be the complex plane. Let $L$ be the infinite straight line in $\C$ wh...")
- 01:46, 13 August 2018 Equation of Imaginary Axis in Complex Plane (hist) [1,722 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\C$ be the complex plane. Let $z \in \C$ be subject to the condition: :$\left\lvert{z - 1}\right\rvert = \left\lvert{z + 1}\r...")
- 18:05, 12 August 2018 Condition for Complex Number to be in Right Half Plane (hist) [749 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\C$ be the complex plane. Let $P$ be the half-plane of $\C$ defined by the Definitio...")
- 17:54, 12 August 2018 Equation of Circle in Complex Plane/Formulation 2/Exterior (hist) [1,253 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\C$ be the complex plane. Let $C$ be a circle in $\C$ whose radius is $...")
- 17:53, 12 August 2018 Equation of Circle in Complex Plane/Formulation 2/Interior (hist) [1,248 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\C$ be the complex plane. Let $C$ be a circle in $\C$ whose radius is $...")
- 17:11, 12 August 2018 Equation of Circle in Complex Plane/Formulation 2 (hist) [1,823 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\C$ be the complex plane. Let $C$ be a circle in $\C$ whose Definition:Radius of Circle|...")
- 07:51, 12 August 2018 Quadratic Equation/Examples/z^4 - 2z^2 + 4 = 0 (hist) [2,495 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Quadratic Equation == <onlyinclude> The quartic equation: :$z^4 - 2 z^2 + 4 = 0$ has the solut...")
- 05:42, 12 August 2018 Sum of Squares of Complex Moduli of Sum and Differences of Complex Numbers (hist) [2,081 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\alpha, \beta \in \C$ be complex numbers. Then: :$\left\lvert{\alpha + \beta}\right\rvert^2 + \left\lvert{\alpha - \beta}\ri...")
- 04:59, 12 August 2018 Quadratic Equation/Examples/z^2 - 4z + 5 = 0 (hist) [1,550 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Quadratic Equation == <onlyinclude> Let the quadratic equation: :$z^2 + b z + c = 0$ have the...")
- 04:46, 12 August 2018 Complex Roots of Polynomial with Real Coefficients occur in Conjugate Pairs/Proof 1 (hist) [1,164 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Complex Roots of Polynomial with Real Coefficients occur in Conjugate Pairs}} == Proof == <onlyinclude> Let $\alpha \in \C$ be a Definition:Root of Polynom...")
- 04:28, 12 August 2018 Quadratic Equation/Examples/z^2 - (3+i)z + 4+3i = 0 (hist) [1,893 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Quadratic Equation == <onlyinclude> The quadratic equation in $\C$: :$z^2 - \left({3 + i}\rig...")
- 19:20, 11 August 2018 Square Root of Complex Number/Examples/3+4i (hist) [1,067 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Square Root of Complex Number == <onlyinclude> :$\sqrt {3 + 4 i} = \pm \left({2 + i}\right)$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \left({x...")
- 19:11, 11 August 2018 Quadratic Equation/Examples (hist) [720 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Quadratic Equation == <onlyinclude> === Example: $x^2 + 1 = 0$ === {{:Quadratic Eq...")
- 19:02, 11 August 2018 Square Root of Complex Number/Examples/2+2i (hist) [1,235 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Square Root of Complex Number == <onlyinclude> :$\sqrt {2 + 2 i} = \pm \left({\dfrac {\sqrt 2} 2 + \dfrac {\sqrt 2} 2 i}\right)$ </onlyinclude> == Proof ==...")
- 18:52, 11 August 2018 Square Root of Complex Number/Examples/i (hist) [1,139 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Square Root of Complex Number == <onlyinclude> :$\sqrt i = \pm $ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \left({x + i y}\right)^2 | r =...")
- 18:30, 11 August 2018 Complex Modulus of Quotient of Complex Numbers/Examples/(1+2i)^12 (1-2i)^-9 (hist) [1,231 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Modulus of Quotient of Complex Numbers == <onlyinclude> :$\left\vert{\dfrac {\left({1 + 2 i}\right)^{12} } {\left({1 - 2 i}\right)^9} }\right\vert =...")
- 18:22, 11 August 2018 Complex Modulus of Quotient of Complex Numbers/Examples (hist) [393 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Modulus of Quotient of Complex Numbers == <onlyinclude> === Complex Modulus of Quotient of Complex Numbers/Examples/(1+2i)^12 (1-2i)^-9|Complex Mo...")
- 18:13, 11 August 2018 Complex Modulus/Examples/1+2it-t^2 over 1+t^2 (hist) [1,135 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Modulus == <onlyinclude> :$\left\vert{\dfrac {1 + 2 i t - t^2} {1 + t^2} }\right\vert = 1$ where: :$t \in \R$ is a Defin...")
- 18:04, 11 August 2018 Complex Modulus of Reciprocal of Complex Number/Examples/5+12i (hist) [890 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Modulus of Reciprocal of Complex Number == <onlyinclude> <onlyinclude> :$\dfrac 1 {5 + 12 i} = \dfrac 1 {13}$ </onlyinclude> == Proof == {{begin-eq...")
- 17:57, 11 August 2018 Complex Modulus of Reciprocal of Complex Number/Examples (hist) [323 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Modulus of Reciprocal of Complex Number == <onlyinclude> === Complex Modulus of Reciprocal of Complex Number/Examples/5+12i|Complex Modulus of $\d...")
- 15:58, 11 August 2018 Power of Complex Modulus equals Complex Modulus of Power/Examples/(2-i)^6 (hist) [930 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Power of Complex Modulus equals Complex Modulus of Power == <onlyinclude> :$\left\vert{\left({2 - i}\right)^6}\right\rvert = 125$ </onlyinclude> == Proof ==...")
- 10:48, 11 August 2018 Complex Modulus/Examples/4+3i (hist) [694 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Modulus == <onlyinclude> :$\left\vert{4 + 3 i}\right\vert = 5$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \lef...")
- 10:09, 11 August 2018 Sum of Arithmetic Progression/Examples/a0 = i, d = 2+2i (hist) [1,297 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Sum of Arithmetic Progression == <onlyinclude> Let $A_n$ be the arithmetic progression of $n$ terms defined as: {{begi...")
- 09:31, 11 August 2018 Complex Algebra/Examples/(z-1) (z-i)^-1 = 2 over 3 (hist) [1,059 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Algebra == <onlyinclude> Let $z \in \C$ be a complex number such that: :$\dfrac {z - 1} {z -...")
- 09:23, 11 August 2018 Complex Algebra/Examples/(2+i)z + i = 3 (hist) [1,214 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Algebra == <onlyinclude> Let $z \in \C$ be a complex number such that: :$\left({2 + i}\right...")
- 09:04, 11 August 2018 Complex Algebra/Examples (hist) [440 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Algebra == <onlyinclude> === Example: $\left({2 - i}\right) z + i = 3$ === {{...")
- 06:29, 11 August 2018 Complex Division/Examples/(1-i) (1+i)^-1 (hist) [872 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Division == <onlyinclude> :$\dfrac {1 - i} {1 + i} = -i$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \dfrac {...")
- 06:23, 11 August 2018 Complex Division/Examples/(3+4i) (1+2i)^-1 (hist) [899 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Division == <onlyinclude> :$\dfrac {3 + 4 i} {1 + 2 i} = \dfrac {11} 5 - \dfrac 2 5 i$ </onlyinclude> == Proof == {{be...")
- 06:09, 11 August 2018 Complex Arithmetic/Examples/(4+2i)^-1 (2-3i)^-1 (hist) [1,471 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Arithmetic == <onlyinclude> :$\dfrac 1 {\left({4 + 2 i}\right) \left({2 - 3 i}\right)} = \dfrac 7 {130} + \dfrac {2 i}...")
- 05:51, 11 August 2018 Power of Complex Number/Examples/(2+i)^4 (hist) [1,180 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Power of Complex Number == <onlyinclude> :$\left({2 + i}\right)^4 = -7 + 24 i$ </onlyinclude> == Proof == We have that: :$\left({2...")
- 05:44, 11 August 2018 Power of Complex Number/Examples (hist) [283 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Power of Complex Number == <onlyinclude> === Example: $\left({2 + i}\right)^4$ === {{:...")
- 05:34, 11 August 2018 Inverse for Complex Multiplication/Examples/3+2i (hist) [825 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Inverse for Complex Multiplication == <onlyinclude> :$\dfrac 1 {3 + 2 i} = \dfrac 3 {13} + \dfrac {2 i} {13}$ </onlyinclude> == Proof == {{begin-eqn}} {{eq...")
- 05:27, 11 August 2018 Complex Multiplication/Examples/(1+2i)(3+4i) (hist) [786 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Complex Multiplication == <onlyinclude> :$\left({1 + 2 i}\right) \left({3 + 4 i}\right) = -5 + 10 i$ </onlyinclude> == Pr...")
- 05:20, 11 August 2018 Complex Multiplication/Examples (hist) [319 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Complex Multiplication == <onlyinclude> === Complex Multiplication/Examples/(1+2i)(3+4i)|Example: $\left({1 + 2 i}\right...")
- 05:15, 11 August 2018 Square Root of Complex Number/Examples/5-12i (hist) [1,017 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Square Root of Complex Number == <onlyinclude> :$\sqrt {5 - 12 i} = \pm \left({3 - 2 i}\right)$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \left(...")
- 19:27, 10 August 2018 Square Root of Complex Number/Examples (hist) [608 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Square Root of Complex Number == <onlyinclude> === Example: $5 - 12 i$ === {{:Square Root of Complex Number...")
- 19:25, 10 August 2018 Square Root of Complex Number (hist) [2,811 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $z = a + i b \in \C$ be a complex number. Let $w = x + i y \in \C$ be such that $w^2 = z$. Then: {{begin-eqn}} {{eqn | l =...")