Question

Write z=-6+6i in polar form

Answer 1

z=r(cosα +i*sinα)
r=√(6²+6²)=√(36+36)=√(2*36)=6√2
tanα=6/-6=-1,  α=135⁰, or  α=3π/4 (if you need in π)

z=6√2(cos 135+i*sin 135)
or
z=6√2(cos 3π/4+i*sin 3π/4)

Answer 2

The polar form of the complex number $Z=-6+6i$ will be

$\rm Z=6\sqrt{2}(cos135+isin135)$

What will be the polar form of the complex number?

The polar form of the complex number  $Z=x+yi$ will be

$\rm Z=r(cos\theta+isin\theta)$

$r=\sqrt{x^2+y^2}$

$\theta= tan^{-1} \dfrac{y}{x}$

So here we have

$Z=-6+6i$

$r=\sqrt{(-6)^2+(6)^2} = 6\sqrt2$

$\theta= tan^{-1} \dfrac{-6}{6} =135^0$

Now the polar form will be

$\rm Z=r(cos\theta+isin\theta)$

$\rm Z=6\sqrt2(cos135+isin 135)$

Thus the polar form of the complex number $Z=-6+6i$ will be

$\rm Z=6\sqrt{2}(cos135+isin135)$

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