91Ó°ÊÓ

To divide complex numbers like \(\frac{-7+4i}{3+2i}\), we use a helpful tool called the conjugate. The conjugate of a complex number is obtained by changing the sign of the imaginary part. For example, the conjugate of \(3+2i\) is \(3-2i\).
The reason we use the conjugate in division is to eliminate the imaginary part of the denominator. By multiplying the numerator and the denominator by the conjugate of the denominator, we can simplify complex fractions more easily. This process converts the denominator into a real number, making the fraction simpler to handle.
In our exercise, multiplying both the numerator and the denominator by \(3-2i\) transforms \(\frac{-7+4i}{3+2i}\) into a format that's easier to simplify.

The distributive property is fundamental when working with complex numbers, especially during multiplication. It states that \(a(b+c) = ab + ac\). When you distribute terms in a complex number multiplication, you apply this property to combine and simplify each part.
In the problem, after multiplying by the conjugate, the numerator \( (-7 + 4i) (3 - 2i)\) gets distributed as follows:
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