Thread: Polar Form and De Moivre's Theorem

Write each formula in polar form..

a) 3-3i
For this, I got sqrt(18)*(cos pi/4 + i sin pi/4)

b) 1-sqrt(3)i
For this, I got 2*(cos 5/3 pi + i sin 5/3 pi)

Use De Moivre's Theorem for:
1-sqrt (3)i

I got 32 (cos 25/3 pi + i sin 25/3 pi) = 32i

Are these correct?

Originally Posted by Jgirl689

Write each formula in polar form..

a) 3-3i
For this, I got sqrt(18)*(cos pi/4 + i sin pi/4)

Modulus is correct. Magnitude of angle is correct. Sign on angle is wrong. It's -pi/4 (3-3i lies in the fourth quadrant in the complex plane)

b) 1-sqrt(3)i
For this, I got 2*(cos 5/3 pi + i sin 5/3 pi)

Yep this is correct.

Use De Moivre's Theorem for:
(1-sqrt (3)i)^5

Judging by your answer put the power in for you.

Your expression is correct, but the final answer is wrong. You'll find that 25pi/3 is equivalent to pi/3

I got 32 (cos 25/3 pi + i sin 25/3 pi) = 32i

Are these correct?

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