# Category:Complex Modulus

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This category contains results about **Complex Modulus**.

Definitions specific to this category can be found in Definitions/Complex Modulus.

Let $z = a + i b$ be a complex number, where $a, b \in \R$.

Then the **(complex) modulus of $z$** is written $\cmod z$ and is defined as the square root of the sum of the squares of the real and imaginary parts:

- $\cmod z := \sqrt {a^2 + b^2}$

## Subcategories

This category has the following 7 subcategories, out of 7 total.

## Pages in category "Complex Modulus"

The following 35 pages are in this category, out of 35 total.

### C

- Complex Modulus equals Complex Modulus of Conjugate
- Complex Modulus equals Zero iff Zero
- Complex Modulus Function is Continuous
- Complex Modulus is Non-Negative
- Complex Modulus is Norm
- Complex Modulus of Additive Inverse
- Complex Modulus of Difference of Complex Numbers
- Complex Modulus of Product of Complex Numbers
- Complex Modulus of Quotient of Complex Numbers
- Complex Modulus of Real Number equals Absolute Value
- Complex Modulus of Reciprocal of Complex Number
- Complex Modulus of Sum of Complex Numbers
- Complex Sequence is Null iff Modulus of Sequence is Null

### M

- Magnitude of Projection of Complex Number on Another
- Modulus and Argument of Complex Exponential
- Modulus in Terms of Conjugate
- Modulus Larger than Imaginary Part
- Modulus Larger than Real Part
- Modulus Larger than Real Part and Imaginary Part
- Modulus of Exponential is Exponential of Real Part
- Modulus of Exponential of i z where z is on Circle
- Modulus of Exponential of Imaginary Number is One
- Modulus of Positive Real Number to Complex Power is Positive Real Number to Power of Real Part
- Modulus of Sum equals Modulus of Distance implies Quotient is Imaginary
- Modulus of Sum equals Modulus of Distance implies Quotient is Imaginary/Corollary
- Modulus z - 1 Less than Modulus z + 1 iff Real z Greater than Zero