Question

Write the complex number in the form a + bi. 6(cos 330° + i sin 330°)

Answer 1

6((√3/2) − (i/2))
6(√3/2) + 6(−i/2)
3√3 + 6(−i/2)
∛3 - 3i

Answer 2

The complex number 6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i

Explanation:

6(cos 330° + i sin 330°)

= 6(cos(360°-30°)+ i sin(360°-30°))

=6(cos30°- i sin30°) (since, 360°-30° lies in fourth quadrant and cos is positive there and sin is negative)

=
`6((√(3))/(2)-i(1)/(2))`

Distributing 6, we get

=3√3-3 i

Hence, the complex number 6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i