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Popular >

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

Solution

simplify

(4 + 3 i)^{- 1}

Solution

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

Solution steps

(4 + 3 i)^{- 1}

Apply exponent rule:

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

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

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

Multiply by the conjugate

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

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

Simplify

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

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

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