Question

You can use this to simplify complex fractions. Multiply the numerator and denominator by the complex conjugate ofthe denominator to make the denominator real.2 + 5i / 1 +3i=

Answer 1

The expression given is

$\frac{2+5i}{1+3i}$

Multiply the numerator and denominator by the complex conjugate of the denominator

Note: The complex conjugate of the denominator is

$1-3i$

Therefore,

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

Expanding the expression

$\frac{2(1-3i)+5i(1-3i)}{1(1-3i)+3i(1-3i)}=\frac{2-6i+5i-15i^2}{1-3i+3i-9i^2}$

Note:

$i^2=-1$

Simplifying the expression

$\begin{gathered} \frac{2-6i+5i-15i^2}{1-3i+3i-9i^2}=\frac{2-i-15(-1)}{1-9(-1)}=\frac{2-i+15}{1+9} \\ \frac{2-i+15}{1+9}=\frac{2+15-i}{10}=\frac{17-i}{10} \\ \frac{17-i}{10}=\frac{17}{10}-\frac{i}{10}=1.7-0.1i \end{gathered}$

Hence, the answer is

$(1.7)+i(-0.1)$