What is the value of a?

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?

All I know is that it equals $\frac{8-i}{3-2i}$ times $\frac{3+2i}{3+2i}$ and then i did not know what to do

Answer 1

Note,

$$\frac{8−i}{3−2i}=\frac{8-i}{3-2i}\cdot\frac{3+2i}{3+2i}=\frac{(24+2)+(16-3)i}{3^2-(2i)^2}=\frac{26+13i}{13}=2+i$$

Answer 2

Hint: This can be written as $$8 +(-\tfrac13)i +(-2)i.$$ Does that help?

Answer 3

$(8-i)(3+2i)$ will be $24+16i-3i+2$ because $i×i=-1$ And $(3-2i)(3+2i)$ [using the identity $(x^2-y^2)=(x-y)(x+y)$] will be $9+4=13$ and then you can separate the fractions with the denominator $13$ and you will get the value of a which will be $26/13=2$.