Question

Divide:$\frac{1+6i}{6-i}$

Short answer

The solution of the above equation is i

Step-by-step solution

Given information

We are given an equation$\frac{1+6i}{6-i}$

Multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a+ibis a-ib

$\frac{1+6i}{6-i}\times \frac{6+i}{6+i}$

Simplify and write results in simple form 

$$\begin{gathered} \frac{6+i+36i-6}{36-i^2} \\ \frac{37i}{37} \\ i \end{gathered}$$

Conclusion

The solution of the above equation is$i$