Question

evaluate the expression \frac{3 - 4i}{4i} and write the result in the form a + bi.

the real number a equals

the real number b equals

question help: video

Explanation:

Multiply numerator and denominator by the imaginary unit

$$ \frac{3 - 4i}{4i} \cdot \frac{i}{i} = \frac{(3 - 4i)i}{4i^2} $$

Simplify using the definition of the imaginary unit

$$
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Separate into real and imaginary parts

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

Answer:

Evaluate the expression \(\frac{3 - 4i}{4i}\) and write the result in the form \(a + bi\).

The real number \(a\) equals <blank>-1</blank>
The real number \(b\) equals <blank>\(-\frac{3}{4}\)</blank>