Answer to Question #173740 in Complex Analysis for Rayhan

Question #173740

Let f(z)=z−1/z+1


. The questions that follow will all revolve around this complex-valued function.

1.

 The value of 25f(2+4i) is equal to a+ib where a,b∈R, and i^2=−1. What is the value of 10a+b?



1
Expert's answer
2021-03-23T05:33:06-0400
"f(z)=z-\\frac{1}{z}+1""f(2+4i)=2+4i-\\frac{1}{2+4i}+1="

"=2+4i-\\frac{2-4i}{(2+4i)(2-4i)}+1="

"=2+4i-\\frac{2-4i} {4+16} +1="

"=2+4i-\\frac{2-4i}{20}+1="

"=2+4i-0.1+0.2i+1="

"=2.9+4.2i"

"25f(2+4i)=25(2.9+4.2i)=72.5+105i"

"a=72.5, b=105"


"10a+b=10\\cdot{72.5}+105=725+105=830"

Answer: 830


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