Question

Use DeMoivres Theorem to find (2cis pi/9)^3

a. 4+4 sqrt 3i
b. 3+3 sqrt 3i
c. 4 sqrt 3+4i
d. 3 sqrt 3+3i

Answer 1

A

Explanation:

Answer 2

The given complex number is:


`(2cis( ( \pi )/(9)))^(3) \\ \\`

cis(x) means cos(x) + i sin(x). So the above expression can be written as:


`(2(cos ( \pi )/(9)+isin ( \pi )/(9)))^(3)`

Using the DeMoivres Theorem we can simplify the expression as:


`(2(cos ( \pi )/(9)+isin ( \pi )/(9)))^(3) \\ \\ =2^(3)(cos(3* ( \pi )/(9))+isin(3* ( \pi )/(9))) \\ \\ =8(cos ( \pi )/(3)+isin ( \pi )/(3)) \\ \\ =8( (1)/(2)+i ( √(3) )/(2)) \\ \\ =4+i4 √(3) \\ \\ =4+4 √(3)i`

So, option A gives the correct answer