Question

How do you write the following quotient in standard form `(8-7i)/(1-2i)`?

Answer 1

22/5+9/5i

Explanation:

Since `(a+b)(a-b)=a^2-b^2 and i^2=-1`,

you can multiply numerator and denominator of the fraction by the expression `(1+2i)` and have:

`((8-7i)(1+2i))/((1-2i)(1+2i))=(8+16i-7i-14i^2)/(1-4i^2)`

`(8+9i+14)/(1+4)=(22+9i)/5=22/5+9/5i`

in standard form