The multiplicative inverse of $(- 2 + 5 i)$ is

(\frac{- 2}{29} + \frac{5}{29} i)

(\frac{2}{29} - \frac{5}{29} i)

(\frac{- 2}{29} - \frac{5}{29} i)

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Text solutionVerified

z = (- 2 + 5 i) \Rightarrow z^{- 1} = \frac{1}{z} = \frac{1}{( - 2 + 5 i )} \times \frac{( - 2 - 5 i )}{( - 2 - 5 i )} = \frac{( 2 - 5 i )}{( 4 - 25 i ^{2} )} = \frac{( - 2 - 5 i )}{( 4 + 25 )} = \frac{( - 2 - 5 i )}{29}

\Rightarrow z^{- 1} = (\frac{- 2}{29} - \frac{5}{29} i)

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Question Text	The multiplicative inverse of $(- 2 + 5 i)$ is
Answer Type	Text solution:1
Upvotes	152