SOLUTION: Express the equation z^4=−2 + 2√3i in polar form. Hence solve the equation, expressing your answers in polar form

, ,  =  =  =  = 
 
.

The reference angle for  is 60° and since x is - and y is +,
 is in the 2nd quadrant, so we subtract 60° from 180° and get
120°, which has the same trig functions as 120° + 360°·k, so we take:

.

Now we have



Now we use the formula: 








Now we let k = 0,1,2,and 3 to get the 4 4th roots, the 4 possible
answers for z:

For k = 0,



For k = 1,



For k = 2,



For k = 3,



Those are the four values for z.

Edwin