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Mathematical expression showing complex number division with imaginary unit i

Handwritten complex number division problem: 4i/(7i) = 4i/7i² = 4i/-7 and 12/(5+i)

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Show Answer Key & Explanations Step-by-step solution for: Dividing Complex Numbers

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- $\frac{4}{7i} \cdot \frac{i}{i} = \frac{4i}{7i^2}$
- $= \frac{4i}{7(-1)} = \frac{4i}{-7}$
- $= -\frac{4i}{7}$

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- $\frac{12}{5+i} \cdot \frac{5-i}{5-i} = \frac{12(5-i)}{(5+i)(5-i)}$
- $= \frac{60 - 12i}{25 - i^2}$
- $= \frac{60 - 12i}{25 - (-1)} = \frac{60 - 12i}{26}$
- $= \frac{60}{26} - \frac{12i}{26} = \frac{30}{13} - \frac{6i}{13}$

Parent Tip: Review the logic above to help your child master the concept of dividing imaginary numbers.

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