How do you plot 5-12i512i and find its absolute value?

1 Answer
Apr 21, 2017

Set up a imaginary coordinate plane and plot the point, the absolute value, or the modulus is the length of the line from (0,0)

Explanation:

An imaginary plane is just like your regular x,yx,y plane but instead of yy in the vertical axis we have ii, starting from 1i,2i, 3i, 4i..., the x axis remains the same. The point 5-12i would be a point that is a value of 5 on the horizontal axis and a value of -12 on the vertical axis, so it'll be a point in the 4th quadrant. You can find the length of this line from 0,0 graphically or algebraically as shown below.

|z| = sqrt(a^2 + b^2) where a is the real part and b the imaginary. So the absolute value of the given term is sqrt(5^2 + (-12)^2) = sqrt(169)