SOLUTION: Calculate square root(1-3i). Give your answer in a+bi form. In polar form use the angle 0&#8804;&#952;<2&#960;.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Calculate square root(1-3i). Give your answer in a+bi form. In polar form use the angle 0&#8804;&#952;<2&#960;.       Log On


   

Question 1083295: Calculate square root(1-3i). Give your answer in a+bi form. In polar form use the angle 0≤θ<2π.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
r=sqrt%28%281%29%5E2%2B%28-3%29%5E2%29=sqrt%281%2B9%29=sqrt%2810%29
and
theta=tan%5E%28-1%29%28-3%2F1%29=tan%5E%28-1%29%28-3%29%29=288.4
So then,
sqrt%281-3i%29=sqrt%28sqrt%2810%29%29%28cos%28288.4%2F2%29%2Bi%2Asin%28288.4%2F2%29%29
sqrt%281-3i%29=sqrt%28sqrt%2810%29%29%28cos%28144.2%29%2Bi%2Asin%28144.2%29%29
Z%5B1%5D=-1.442%2B1.040i
and


Z%5B2%5D=1.442-1.040i