Question

find the standard form of the complex number shown below

9(cos 11pi/6 + isin 11pi/6)

a. 2/9 - 2(squareroot)3/9 i
b. -4(squareroot)3/9 + 4/9 i
c. 9/2 - 9(squareroot)3/2 i
d. 9(squareroot)3/2 - 9/2 i
e. -9(squareroot)3/4 - 9/4 i

Answer 1

just evaluate, even if you don't have a calculator, you should be able to find
cos 11π/6 or cos 330° = cos30° = √3/2
sin 11π/6 = -1/2

9(cos 11pi/6 + i sin 11pi/6)
= 9(√3/2 - 1/2)
= 9√3/2 - 9/2 i