Chapter 4.8, Problem 66STP

To determine

To Find: The simplified solution of given equation.

Answer to Problem 66STP

  $\frac{9+7i}{15}$

Explanation of Solution

Given:

  $\frac{5+i}{6-3i}$

Formula Used:

  $\begin{array}{l}\text{Rationalisation of fraction}\\ \frac{a-b}{c+d}=\frac{a-b}{c+d}\times \frac{c-d}{c-d}\\ or\\ \frac{a-b}{c+d}=\frac{a-b}{c+d}\times \frac{a+b}{a+b}\end{array}$

Calculation:

  $\begin{array}{l}\frac{5+i}{6-3i}\\ \text{On rationalising the denominator}\text{.}\\ =\frac{5+i}{6-3i}\times \frac{6+3i}{6+3i}\\ =\frac{\left(5+i\right)\left(6+3i\right)}{\left(6-3i\right)\left(6+3i\right)}\\ =\frac{30+6i+15i-3}{36+9}\\ =\frac{27+21i}{45}\\ =\frac{9+7i}{15}\end{array}$

Conclusion:

Thus the simplified form of the given equation is $\frac{9+7i}{15}$ .