Question

If the expression $\frac{2-i}{5-2i}$ is reduced to $(a+bi)$, where $a,b$ are real numbers, then the value of $-b$ is

• A. $\frac{1}{29}$
• B. $-\frac{1}{29}$
• C. $-29$
• D. $29$

Answer 1

The correct option is A $\frac{1}{29}$

The value of $\frac{2-i}{5-2i}$

$=\frac{2-i}{5-2i}\times \frac{5+2i}{5+2i}$

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

$=\frac{10+4i-5i+2}{25+4}$

$=\frac{12-i}{29}$

$=\frac{12}{29}-\frac{i}{29}$

After comparing this with $a+ib$, we get

$\therefore a=\frac{12}{29},b=\frac{-1}{29}$

$\therefore -b=\frac{1}{29}$