How would I use the De.M Theorem to find the power given below?

Question

[ 3 ( cos 3π/8 + i sin 3π/8 ) ] ⁴

^{how also, would I write this in rectangular form? Using the DeMoivre’s Theorem Thank you.}

Answer 1

You take the constant to the power and multiply the angle by the power.

Thus, as 3π/8 * 4 = 3π/2,

[ 3 ( cos 3π/8 + i sin 3π/8 ) ] ⁴ =

3⁴ [( cos 3π/2 + i sin 3π/2)] =

81 [cos 270° + i sin 270° ] =

81[0 + i * -1] =

-81i

Answer 2

3⁴ (cos (4)(3π/8)) + i sin (4)(3π/8))

81 (cos 3π/2 + i sin 3π/2)

81 (0 + i (-1))

-81i