Question

If $x$ and $y$ are real numbers such that $\frac{1+3i}{2-5i}+\frac{1-5i}{2+5i}=x+yi$, then

• A. $x=\frac{-36}{29},y=\frac{-}{4}29$
• B. $x=\frac{-26}{21},y=\frac{31}{21}$
• C. $x=\frac{-36}{29},y=\frac{-2}{29}$
• D. Non of these

Answer 1

Answer: (A)

$x=\frac{-36}{29},y=\frac{-}{4}29$

We have,

$\frac{1+3i}{2-5i}+\frac{1-5i}{2+5i}=x+iy$

$\Rightarrow \frac{\left(2+6i+5i-15\right)+(2-5i-10i-25)}{\left(2-5i\right)\left(2+5i\right)}=x+iy$

$\Rightarrow \frac{-13+11i-15i+23}{29}=x+iy$

$\frac{-36-4i}{29}=x+iy$

$x=\frac{-36}{29},y=\frac{-4}{29}$