Convert from polar to rectangular form 24(cos pi/6 + i sin pi/6)

Question

Please show steps, thank you.

Answer 1

Need be familiar with the unit circle.

So π/6=30° and on the unit circle at π/6 or 30° there is a coordinate that says (√3/2,1/2)

The coordinates correspond to (cos θ, sinθ) so this means that at cos(π/6) or cos30°= √3/2

and with sin(π/6) or sin30°=1/2

So,

24(cos π/6+ i*sin π/6)

=24(√3/2+ i*1/2)

=12(√3+i)