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

1 Answer
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 3-7i, 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.