Question

Write the complex number in the form a + bi.

3(cos 60° + i sin 60°)

Answer Choices
square root three divided by six plus square root of three divided by six times i

square root three divided by two plus three times square root three divided by two times i

three divided by two plus three square root three divided by two times i

square root of three + i

Answer 1

`(3)/(2)` +
`(3√(3) )/(2)` i

Explanation:

Using the exact value

cos60° =
`(1)/(2)` and sin60° =
`(√(3) )/(2)`, then

3(cos60° + isin60°)

= 3(
`(1)/(2)` +
`(√(3) )/(2)` i) ← distribute by 3

=
`(3)/(2)` +
`(3√(3) )/(2)` i ← in the form a + bi