Question

The conjugate of the complex number $\frac{2+5i}{4-3i}$ is equal to:

• A. $\frac{7-26i}{25}$
• B. $\frac{-7-26i}{25}$
• C. $\frac{-7+26i}{25}$
• D. $\frac{7+26i}{25}$

Answer 1

Answer: (C)

Let $z=\frac{2+5i}{4-3i}$ Rationalize $=\frac{2+5i}{4-3i}\times \frac{4+3i}{4+3i}$
$=\frac{8+26i-15}{(4{)}^2-(3i{)}^2}=\frac{8+26i-15}{16+(9)}=\frac{-7+26i}{25}$