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

1 Answer
Y
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.

Related questions
See all questions in Complex Number Plane
Impact of this question
4495 views around the world
You can reuse this answer
Creative Commons License