How do you convert $5 sqrt 3 - 5i$ to polar form?

Question

12094 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-30T06:44:35

The answer is $=10(cos(-pi/6)+isin(-pi/6))$

Let $z=5sqrt3-5i$

We must transform this equation to the form

$z=r(cos theta+isintheta)$

We calculate the modulus of $z$

$∣z∣=sqrt(25*3+25)=sqrt100=10$

$z=∣z∣((5sqrt3)/(∣z∣)-i5/(∣z∣))$

$z=10(5sqrt3/10-i5/10)$

$z=10(sqrt3/2-1/2i)$

Therefore,

$costheta=sqrt3/2$ and $sintheta=-1/2$

We are in the 4th quadrant

$theta=-pi/6$

Therefore,

$z=10(cos(-pi/6)+isin(-pi/6))$

$z=e^((-ipi)/6)$

How do you convert 5 sqrt 3 - 5i5 sqrt 3 - 5i to polar form?