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.