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

`(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,

`(2+5i)/(1+3i)*(1-3i)/(1-3i)=((2+5i)(1-3i))/((1+3i)(1-3i))`

Expanding the expression

`(2(1-3i)+5i(1-3i))/(1(1-3i)+3i(1-3i))=(2-6i+5i-15i^2)/(1-3i+3i-9i^2)`

Note:

`i^2=-1`

Simplifying the expression

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

Hence, the answer is

`(1.7)+i(-0.1)`