How do you find the absolute value of the complex number -4+i?

1 Answer
Oct 9, 2015

Take the square root of the sum of the real part squared plus the imaginary part squared.

Explanation:

For real numbers, we find the distance of the number from 0 on the x-axis.

In this case, we have a complex number with a real part and an imaginary part. On a coordinate plane, we would use the y-axis as the imaginary axis 'i' and plot this complex number at (-4, 1).

Next, find the distance of that point from zero. To do that, we'd use the Pythagorean Theorem. Imagine the x-axis (from (0,0) to (0, -4) as one leg of the triangle, a, and the straight line parallel to the y- (or i-axis from (-4, 0) to (-4, 1) as the second leg, b. The hypotenuse, c, will then be the straight line going from (0,0) to (4, -1).

So, solving for c in the equation a^2 + b^2 = c^2, we take the square root of both sides.

sqrt(c^2) = sqrt(-4^2 + 1^2)

c = sqrt(16 + 1)

c = sqrt(17)

Therefore, abs(-4 + i) = sqrt(17).