Question

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

• A. $\frac{2+3i}{4-i}$
• B. $\frac{11+10i}{17}$
• C. $\frac{11-10i}{17}$
• D. $\frac{2+3i}{4i}$

Answer 1

The correct option is B $\frac{11+10i}{17}$

Rationalize the given complex number by multiplying both the numerator and the denominator with $4+i$.

$\frac{2-3i}{4-i}$ $\times$ $\frac{4+i}{4+i}$ = $\frac{8-10i+3}{16+1}$ = $\frac{11-10i}{17}$

Its conjugate is $\frac{11+10i}{17}$.