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

Question 1181505: Given z = (1+i)/(√2), find (z)^(3/2)
Answer by ikleyn(52903) (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   radians, or 45°.


Therefore,  z =  = cis(45°).



It implies  (z)^3 =  = cis(135°).



Therefore,  (z)^(3/2) =  = cis(67.5°).      ANSWER

Solved, answered and carefully explained.

RELATED QUESTIONS
1+Z+Z^2+Z^3...=1/Z-1 (answered by richard1234)

Solve for Z:... (answered by MathLover1)

Solve for z:... (answered by Seutip)

Find the principal argument Arg(z) 1. z=i/-2-2i 2. z=(√3... (answered by solver91311)

z is the complex number 1+i, where i^2=-1. (i) Find z^2 and z^3. (ii) Verify that... (answered by ewatrrr)

3(z-2)=2(z-1) (answered by j1mmy94)

2|z+1|-3=z-2 (answered by MathLover1)

2|z+1|-3=z-2 (answered by stanbon)

How do I simplify the expression? z^5/2 z^-1/2 \... (answered by MathLover1)