Question

Express $\frac{15 + 10i}{1 + 2i}$ in rectangular form.

Answer 1

7-4i

Explanation:

Multiplying the numerator and denominator by $1-2i$ gives

\begin{align*}

\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\

&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\

&= \frac{5(3 + 2i)(1 - 2i)}{5} \\

&= (3 + 2i)(1 - 2i) \\

&= 3 + 2i - 6i - 4i^2 \\

&= 3 + 2i - 6i + 4 \\

&= \boxed{7 - 4i}.

Answer 2

`(15 + 10i)/(1 + 2i)=\\\\((15 + 10i)(1-2i))/((1 + 2i)(1-2i))=\\\\(15-30i+10i+20)/(1+4)=\\\\(35-20i)/(5)=\\\\7-4i`