Urgent math help!?

Question

Find the a+bi form of a number in trigonometric form

(square root of 7) (cos(pi/12)+isin(pi/12)

What do you do to solve this problem? What is the answer?

Thanks

pi as in 3.14...

Need the exact answer

Answer 1

seems like an euler relationship problem to me.

essentially, you have...
|r| exp(j*theta) = r [ cos(theta) + j sin(theta) ]
so, you have sqrt(7) for a magnitude, and pi/12 for theta

in polar form, you end up with...
sqrt(7) angle pi/12 radians

to convert to rectangular form,
x = r cos(theta)
y = r sin(theta)

cos(pi/12) = .966
sin(pi/12) = .259
sqrt(7) = 2.646

so your answer is approximately (2.556, 0.685)

Answer 2

√7 cos(π/12) = 2.5556
i√7 sin(π/12) = 0.6848i

so you get 2.5556 + 0.6848i

Answer 3

You multiply it out:
√7 cos(π/12) = 2.5556
i√7 sin(π/12) = 0.6848i

so you get 2.5556 + 0.6848i