Complex Number Formula


Posted in Math Formulas




Complex number Formula

A complex number is one of the form of a + ib, where a and b are real number and i = \sqrt{-1}. A is called real part of the complex number and b is called imaginary part of the complex number.

1.De movre’s Theorem

De Movre’s Theorem is a relatively simple formula for calculating powers of complex numbers. De movre’s theorem states that for any positive integer \{r(\cos[r(\cos \theta + I \sin \theta)]^n = r^n (\cos \theta + I \sin \theta)

2.Square root of complex number

x^2 = \dfrac{\sqrt{a^2 + b^2} + a}{2} and y^2 = \dfrac{\sqrt{a^2 + b^2}- a}{2}

For (x + iy)^2 = a + ib.

3.Cube root of unity.


Let For z^3 = 1 the requrd cube root of unity are
1, \dfrac{-1 + \sqrt{3i}}{2} \& \dfrac{-1- \sqrt{3i}}{2} or 1, \omega, \omega^2 (\omega = omega)

Note:

i.1 + \omega + \omega^2 = 0 \\[3mm]

ii. \omega.\omega^2 = 1

iii.\omega^3n = 1 for any integer n.



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