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.

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