Convert given two complex number division into polar form

Question

Sorry if I am breaking any rule. But I really need help with polar form because I have an exam Tomorrow.

Suppose $z=1+i$ and $w=1−i\sqrt3$. Write $q=z^6/w^5$ in polar form and calculate its modulus.

What I have tried so far: First, I found z

z=$√2(\cos \Pi/4+ i sin \Pi/4)$

then W

r = $√(1+3) = 2$ z=$√2(\cos\theta + i sin\theta)$

but I don't know how to find theta here.

Thanks in advance!

Answer 1

Asked : $z=1+iz=1+i$

$w=1−i3$

$q=z^6/w^5$

1.) Calculate the exponential form of q

2.) Calculate the modulus

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1.)

$z = √2(cos(\pi/4)+ isin(\pi/4), z= \sqrt2e\^(i\pi/4)$ $w = √2(cos(-\pi/3)+ isin(-\pi/3), w= \sqrt2e\^(-i\pi/4)$

$z^6 = 8e\^(i3/2\pi)$

$w^5=32e\^(-i5/3\pi9$

$q= 1/4e\^(i19/6\pi)$

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2.) $|q|= 1/4$

Answer 2

HINT

Write z and w in exponential form then compute $z^6$ and $w^5$ then divide.