Multiplicative Inverses of Complex Numbers

Once you have understood division of complex numbers and how to use conjugates to remove iota from the denominator, finding multiplicative inverse of a given complex number is straightforward. Try these questions.

To find the multiplicative inverse, take the following four steps.

First Step: Take Reciprocal: $\dfrac{1}{a+bi}$
Second Step: Multiply and Divide by Conjugate: $\dfrac{1}{a+bi} \cdot \dfrac{a-bi}{a-bi}$
Third Step: Multiply and Simplify: $\dfrac{a-bi}{a^2+b^2}$
Fourth Step: Separate Real and Imaginary Term: $\dfrac{a}{a^2+b^2} - \dfrac{b}{a^2+b^2}i$

Good luck! Get all questions correct to pass this lesson.

Find Multiplicative Inverse Of

$z = 6 + 8i$

Find Multiplicative Inverse Of

$z = -6 + 12i$

Find Multiplicative Inverse Of

$z = 12 - 10i$

End of Lesson

Multiplicative Inverses of Complex Numbers

To find the multiplicative inverse, take the following four steps.

First Step: Take Reciprocal:

\dfrac{1}{a+bi}

Second Step: Multiply and Divide by Conjugate:

\dfrac{1}{a+bi} \cdot \dfrac{a-bi}{a-bi}

Third Step: Multiply and Simplify:

\dfrac{a-bi}{a^2+b^2}

Fourth Step: Separate Real and Imaginary Term:

\dfrac{a}{a^2+b^2} - \dfrac{b}{a^2+b^2}i

Good luck! Get all questions correct to pass this lesson.

Find Multiplicative Inverse Of

$z = 6 + 8i$

Find Multiplicative Inverse Of

$z = -6 + 12i$

Find Multiplicative Inverse Of

$z = 12 - 10i$