How do you simplify $(3-2i)/(1- i)$ and write in a+bi form?

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Answer 1 · 2016-02-26T04:02:41

$5/2-1/2i$

To simplify $(3−2i)/(1−i)$ and write in a+bi form

we need to multiply and divide the fraction by denominator's complex conjugate i.e. $1+i$ . The fraction then becomes

$((3−2i)(1+i))/((1−i)(1+i)$ or

$(3+3i-2i-2i^2)/(1^2-i^2)$ and now using $i^2=-1$ , this becomes

$(5-i)/2$ or $5/2-1/2i$

How do you simplify (3-2i)/(1- i)(3-2i)/(1- i) and write in a+bi form?