# How do you find the magnitude of 3 - 7i?

May 16, 2017

Answer: $\sqrt{58}$

#### Explanation:

The magnitude of a value is the absolute value.

The absolute value of any number is its distance from 0.

In this case, we have a complex number with real value of 3 and imaginary value of -7. In the complex number plane, the "x-axis" is the real axis while the "y-axis" is the imaginary axis.

Therefore, to find the magnitude of $3 - 7 i$, we make a right triangle with horizontal side length of $3$ and vertical side length of $7$, for which we can use Pythagorean's Theorem to find the magnitude:
$\sqrt{{3}^{2} + {7}^{2}}$
$= \sqrt{9 + 49}$
$= \sqrt{58}$
which does not have any squares, so this is our answer.