Question

Find the multiplicative inverse of the following; 

1. 3 – 4i

2. 2 – 3i

3. √5 + 3i

Answer 1

1. Multiplicative inverse =  \(\frac{1}{3-4i}\)

= \(\frac{1}{3-4i}\)\(\times \frac{3 + 4i}{3+4i}\) = \(\frac{3 + 4i}{9+16}\) = \(\frac{3+4i}{25}\)

2. Multiplicative inverse = \(\frac{1}{2-3i}\)

\(\frac{1}{2-3i} \times \frac{2+3i}{2+3i}\) = \(\frac{2+3i}{4+9}\) = \(\frac{2+3i}{13}\)

3. Multiplicative inverse = \(\frac{1}{\sqrt{5}+3i}\)

\(\frac{1}{\sqrt{5} + 3i} \times \frac{\sqrt 5 -3i}{\sqrt5 + 3i}\) = \(\frac{\sqrt{5} - 3i}{5+9}\) = \(\frac{\sqrt{5} - 3i}{14}\)