Question

$\frac{8-i}{3-2i}$
If the expression above is rewritten in the form $a+bi$, where $a$ and $b$ are real numbers, what is the value of $a$? (Note: $i=\sqrt{-1}$)

• A. $2$
• B. $\frac{8}{3}$
• C. $3$
• D. $\frac{11}{3}$

Answer 1

The correct option is A $2$

Given expression $\frac{8-i}{3-2i}$

Rationalising the denominator, we get
$\frac{8-i}{3-2i}=\frac{(8-i)(3+2i)}{(3-2i)(3+2i)}$

$=\frac{(24+16i-3i+2)}{(9+4)}$

$=\frac{26+13i}{13}=2+i$
Hence, $a=2$