Question

1. multiply -7 + 6i by its conjugate.

product =

Explanation:

Step1: Find the conjugate

The conjugate of $-7 + 6i$ is $-7-6i$.

Step2: Multiply the complex - number and its conjugate

\[

$$\begin{align*} (-7 + 6i)(-7-6i)&=(-7)^2-(6i)^2\\ &=49-36i^2 \end{align*}$$

\]
Since $i^2=-1$, we have:
\[

$$\begin{align*} 49-36i^2&=49-36\times(-1)\\ &=49 + 36\\ &=85 \end{align*}$$

\]

Answer:

85