How Do You Convert a Complex Number to Polar Form?

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Hello, first of all lovely forums you have here. I would love to get some help with this task please.

Task:

In this exercise is z = -2 + 2i√3.

a) Find the polar coordinates of z.
b) Find z^22 and enter the number of the form a + ibThank you,

Greetings
 
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Welcome to PH Forums.

Please show what you have tried and where you are stuck so that we can help you.
 
polar form of a complex number is

z=re^{i \theta}

so you have to convert your number in this form. To do it, use Euler's formula

http://en.wikipedia.org/wiki/Euler's_formula
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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