SOLUTION: Given z = (1+i)/(√2), find (z)^(3/2)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given z = (1+i)/(√2), find (z)^(3/2)      Log On


   

Question 1181505: Given z = (1+i)/(√2), find (z)^(3/2)
Answer by ikleyn(52893) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given z = (1+i)/(√2), find (z)^(3/2)
~~~~~~~~~~~~~~~~~~~~ 

Notice that this complex number has the modulus equal to 1 (one) and the argument of pi%2F4  radians, or 45°.


Therefore,  z = cis%28pi%2F4%29 = cis(45°).



It implies  (z)^3 = cis%283pi%2F4%29 = cis(135°).



Therefore,  (z)^(3/2) = cis%283pi%2F8%29 = cis(67.5°).      ANSWER

Solved, answered and carefully explained.