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Popular >

simplify (3+4i)^{-1}

Solution

simplify

(3 + 4 i)^{- 1}

Solution

\frac{3}{25} - \frac{4}{25} i

Solution steps

(3 + 4 i)^{- 1}

Apply exponent rule:

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

(3 + 4 i)^{- 1} = \frac{1}{3 + 4 i}

= \frac{1}{3 + 4 i}

Multiply by the conjugate

\frac{3 - 4 i}{3 - 4 i}

= \frac{1 \cdot ( 3 - 4 i )}{( 3 + 4 i ) ( 3 - 4 i )}

Simplify

\frac{1 \cdot ( 3 - 4 i )}{( 3 + 4 i ) ( 3 - 4 i )} : \frac{3 - 4 i}{25}

= \frac{3 - 4 i}{25}

Rewrite in standard complex form:

\frac{3}{25} - \frac{4}{25} i

= \frac{3}{25} - \frac{4}{25} i

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Frequently Asked Questions (FAQ)

What is (3+4i)^{-1} ?
The solution to (3+4i)^{-1} is 3/25-4/25 i