Question

Which can be used to find the absolute value of 4 – 7i?

Answer 1

Answer: $|4 - 7i|=\sqrt{4^2+(-7)^2}$

Step-by-step explanation:

By definition, the absolute value of a complex number is the measure of its distance from zero on the complex number plane.

You need to use the following formula:

$|a+bi|=\sqrt{a^2+b^2}$

Then, knowing the formula and given the following complex number:

$4 - 7i$

You can identify that:

$a=4\\\\b=-7$

Then, the next step is to substitute those values into the formula.

So you get:

$|4 - 7i|=\sqrt{4^2+(-7)^2}=\sqrt{65}$

Therefore, as you can notice in the procedure above, you can use $\sqrt{4^2+(-7)^2}$ to find the absolute value of the complex number $4 - 7i$.