absolutestylehc

2022-02-02

How do you find the product of the complex number and its conjugate of $-7+\sqrt{13i}$?

Devyn Figueroa

Expert

Step 1
The given complex number is $-7+i\sqrt{13}$
The conjugate of the given number is $-7-i\sqrt{13}$
The product:
$=\left(-7+i\sqrt{13}\right)\left(-7-i\sqrt{13}\right)={\left(-7\right)}^{2}-{\left(i\sqrt{13}\right)}^{2}$
$=49-13{i}^{2}=49-\left(-13\right)$
$=49+13=62$

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