https://file.aiquickdraw.com/mathbot/file/1727297652843z8cziouh.jpg

The expression in the image is:

\[
\frac{5i}{-7 + 8i}
\]

To simplify this, we'll multiply both the numerator and the denominator by the complex conjugate of the denominator, which is \(-7 - 8i\). This removes the imaginary part from the denominator.

Let me perform the calculation.

\[
\frac{5i}{-7 + 8i} \times \frac{-7 - 8i}{-7 - 8i} = \frac{5i(-7 - 8i)}{(-7 + 8i)(-7 - 8i)}
\]

Let's compute both the numerator and the denominator separately. I'll handle this now.

Learn how to simplify the complex number expression 5i / (-7 + 8i) by multiplying with the conjugate. This step-by-step solution involves key concepts in complex numbers and conjugates, suitable for Grades 10-12.

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