Question

Use the complex conjugate to find the absolute value of 8+12i

Answer 1

8 + 12i × ( 8 - 12i / 8 - 12i )
= 64 - 144i^2 / 8 - 12i
= 64 - 144(-1) / 8 - 12i
= 64 + 144 / 8 - 12i
= 208 / 8 - 12i
= 26 - 52/3i

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Answer 2

Since the problem is asking us to do so, we are going to use the complex conjugate formula to find the absolute value of our complex number.

The complex conjugate formula is: $|z|=\sqrt{z(conjugate.of .z)}$

where

$z$ is the complex number

$|z|$ is the absolute value of the complex number

We know from our problem that our complex number is $8+2i$, so $z=8+2i$. Now to conjugate of our complex number, we just need to change the sign of the imaginary part:

$conjugate=8-2i$

Now that we have all we need, let's replace the values in our formula:

$|z|=\sqrt{z(conjugate.of .z)}$

$|8+2i|=\sqrt{(8+2i)(8-2i)}$

$|8+2i|=\sqrt{64-16i+16i-4i^2}$

$|8+2i|=\sqrt{64-4i^2}$

$|8+2i|=\sqrt{64+4}$

$|8+2i|=\sqrt{68}$

$|8+2i|=2\sqrt{17}$

We can conclude that the absolute value of $8+2i$ is $2\sqrt{17}$