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

Question

Find the multiplicative inverse of 2 - 3i.

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Answer

Let z = 2 - 3i
Then, $\overline { z }$ = 2 + 3i
and |z|² = 2² + (- 3)² = 4 + 9 = 13
Therefore, the multiplicative inverse of 2 - 3i is given by
z^-1 = $\frac { \overline { z } } { | z | ^ { 2 } } = \frac { 2 + 3 i } { 13 } = \frac { 2 } { 13 } + \frac { 3 } { 13 } i$

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