Question

Find the multiplicative inverse of $2 - 3i$.

• A. $2/13+i(3/13)$
• B. $2/13-i(3/13)$
• C. $2+3i$
• D. None of these

Answer 1

Answer: (A)

$2/13+i(3/13)$

Answer 2

Let $z = 2-3i$ , then, $z^{-1}=\frac{1}{2-3i}$ $=\frac{2+3i}{\left(2-3i\right)\left(2+3i\right)}$ $=\frac{2+3i}{2^{2}-\left(3i\right)^{2}}$ $=\frac{2+3i}{13}$ $=\frac{2}{13}+\frac{3}{13} i$