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Popular >

simplify (2-3i)^{-1}

Solution

simplify

(2 - 3 i)^{- 1}

Solution

\frac{2}{13} + \frac{3}{13} i

Solution steps

(2 - 3 i)^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(2 - 3 i)^{- 1} = \frac{1}{2 - 3 i}

= \frac{1}{2 - 3 i}

Multiply by the conjugate

\frac{2 + 3 i}{2 + 3 i}

= \frac{1 \cdot ( 2 + 3 i )}{( 2 - 3 i ) ( 2 + 3 i )}

Simplify

\frac{1 \cdot ( 2 + 3 i )}{( 2 - 3 i ) ( 2 + 3 i )} : \frac{2 + 3 i}{13}

= \frac{2 + 3 i}{13}

Rewrite in standard complex form:

\frac{2}{13} + \frac{3}{13} i

= \frac{2}{13} + \frac{3}{13} i

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Frequently Asked Questions (FAQ)

What is (2-3i)^{-1} ?
The solution to (2-3i)^{-1} is 2/13+3/13 i