Question

Find the product of (-1-3i) and its conjugateProduct=

Answer 1

Step-by-step explanation

To find the complex conjugate of -1-3i we change the sign of the imaginary part. Therefore, the conjugate is -1+3i

We can then find the product of -1-3i and its conjugate -1+3i below.

`\begin{gathered} \mathrm{Apply\:complex\:arithmetic\:rule}:\quad \left(a+bi\right)\left(a-bi\right)=a^2+b^2 \\ a=-1,\:b=-3 \\ =\left(-1\right)^2+\left(-3\right)^2 \\ =1+9 \\ =10 \end{gathered}`

Answer: 10