SOLUTION: Hi! I can't seem to figure out how to solve this question: The complex number z is a solution of the equation {{{ sqrt( z )= 4/(1+i) + 7 - 2i }}}. Express z in the form a+bi wh

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi! I can't seem to figure out how to solve this question: The complex number z is a solution of the equation {{{ sqrt( z )= 4/(1+i) + 7 - 2i }}}. Express z in the form a+bi wh      Log On


   

Question 1097117: Hi!
I can't seem to figure out how to solve this question:
The complex number z is a solution of the equation +sqrt%28+z+%29=+4%2F%281%2Bi%29+%2B+7+-+2i+. Express z in the form a+bi where a and b are integers.
Thank you!
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
4/(1+i) = 4(1-i)/((1+i)(1-i)) = (4 - 4i)/(1 - i^2) = (4 - 4i)/2 = 2 - 2i
So we have sqrt(z) = 2 - 2i + 7 - 2i = 9 - 4i
Now square both sides:
z = (9-4i)^2 = 81 - 72i + 16i^2 = 81 - 16 - 72i = 65 - 72i
Ans: z = 65 - 72i