Write the complex number in trigonometric form r(cos theta + I sin theta ) with theta in the interval (0,2pi).

Question

12) 3i. 3i is the problem i am trying to answer please help me not sure how to do it. It's pre calcus.

Answer 1

interval (0,2Pi) says anywhere on the circle

3i = (0 + 3i)  there is no real part or real part = 0

so for the real part (which is graphed on the x axis) to be 0 the point lies somewhere on the y axis

indeed 3i is on the y (or imaginary) axis and is 3 units up.

This means it is at an angle of 90 degrees  and has a length of 3.

so r = 3 and θ = 90

 

Therefore 3i = 3[cos(90) + i sin(90)]