Question

If $A+iB=\frac{4+2i}{1-2i}$ where $i=\sqrt{-1}$, then what is the value of A?

• A. -8
• B. 0
• C. 4
• D. 8

Answer 1

The correct option is B 0

$A+iB=\frac{4+2i}{1-2i}\Rightarrow A+iB=\frac{4+2i}{1-2i}\times \frac{1+2i}{1+2i}\Rightarrow A+iB=\frac{(4-4)+i(4\times 2+2)}{1^2+2^2}\Rightarrow A+iB=\frac{0+10i}{5}=2i$

By comparing real and imaginary terms, we get

Value of $A=0$ and $B=2$