Category:Square Root of Complex Number in Cartesian Form
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This category contains pages concerning Square Root of Complex Number in Cartesian Form:
Let $z \in \C$ be a complex number.
Let $z = x + i y$ where $x, y \in \R$ are real numbers.
Let $z$ not be wholly real, that is, such that $y \ne 0$.
Then the square root of $z$ is given by:
- $z^{1/2} = \pm \paren {a + i b}$
where:
| \(\ds a\) | \(=\) | \(\ds \sqrt {\frac {x + \sqrt {x^2 + y^2} } 2}\) | ||||||||||||
| \(\ds b\) | \(=\) | \(\ds \frac y {\cmod y} \sqrt {\frac {-x + \sqrt {x^2 + y^2} } 2}\) |
Pages in category "Square Root of Complex Number in Cartesian Form"
The following 3 pages are in this category, out of 3 total.