SOLUTION: how do you undo rcis theta? if you have a problem such as 4(cos pi/4 + i sin pi/4) how would you put that back into a +bi? im not asking for an answer, rather the method to do t

Algebra ->  Trigonometry-basics -> SOLUTION: how do you undo rcis theta? if you have a problem such as 4(cos pi/4 + i sin pi/4) how would you put that back into a +bi? im not asking for an answer, rather the method to do t      Log On


   

Question 293596: how do you undo rcis theta?
if you have a problem such as 4(cos pi/4 + i sin pi/4) how would you put that back into a +bi?
im not asking for an answer, rather the method to do the problem
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: For any polar number in the form z=r%28cos%28x%29%2Bi%2Asin%28x%29%29, where 'r' is the magnitude and 'x' is the angle, it can be converted into rectangular form a%2Bbi using the following equations:


1) r=sqrt%28a%5E2%2Bb%5E2%29 (this can be seen if you draw out a triangle with sides 'a', 'b', and hypotenuse 'r')

2) tan%28x%29=b%2Fa (again this can be seen with a drawing of the triangle) Note: since 'b' is the vertical side, this is the side opposite from the angle 'x'


So in this case, r=4 and x=pi%2F4 meaning that 4=sqrt%28a%5E2%2Bb%5E2%29 and tan%28pi%2F4%29=b%2Fa. You'll then find that you'll have two equations and two unknowns which means that you can solve for both 'a' and 'b'.