Question

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

• A. $\frac{726i}{25}$
• B. $\frac{-726i}{25}$
• C. $\frac{-7+26i}{25}$
• D. $\frac{7+26i}{25}$

Answer 1

The correct option is C $\frac{-7+26i}{25}$

Conjugate of $\frac{2+5i}{4-3i}$

$=\frac{(2+5i)(4+3i)}{(4-3i)(4+3i)}$

$=\frac{8+6i+20i-15}{{\left(4\right)}^2-{\left(3i\right)}^2}$

$=\frac{-7+26i}{25}$

Hence, the answer is $\frac{-7+26i}{25}.$