Question

HELP please.........
For questions 16 - 19, write each expression in the standard form for the complex number a + bi.
16. [ 4 ( cos (7pi/9) + i sin (7pi/9) ]^3

17. [ 1/2 ( cos (72) + i sin (72) ) ]^5

18. The complex fifth roots of 5 - 5 sqrt (3) i.

19. Find all seventh roots of unity

Answer 1

He means:
= 4^3 cis ( 3 * 7 pi/9)

Answer 2

64+7pi/3

Answer 3

\[(r \angle \theta )^{n} = r ^{n} \angle n \theta\]
16. First, convert to a+ib polar form

Answer 4

= 64 ( 1/2 + i√3/2)
= 32 + 32√3i

Answer 5

16. \[e ^{i \theta} = \cos( \theta )+isin(\theta)\]
\[[ 4 ( \cos (7\pi/9) + i \sin (7\pi/9) ] = 4e ^{i (7\pi/9)}\]
\[[ 4 ( \cos (7\pi/9) + i \sin (7\pi/9)]^3 = (4e^{i(7\pi/9)})^{3}\]
\[(4e^{i(7 \pi/9)})^3 = 4^{3}* e^{i(3*7\pi/9)} = 64e^{i(7\pi/3)}\]