Question 246785
I think your answer is here.


<a href = "http://www.regentsprep.org/rEGENTS/mathb/3C6/absvlecomlesson.htm" target = "_blank">http://www.regentsprep.org/rEGENTS/mathb/3C6/absvlecomlesson.htm</a>


-5 + 12i is equivalent to a + bi where:


a = -5
b = 12


|-5+12i| = |z| where |z| = sqrt(a^2 + b^2) = sqrt((-5)^2 + 12^2) = sqrt (25 + 144) = sqrt (169) = 13


Apparently you are talking about a complex plane where the x-axis is the real part and the y-axis is the imaginary part of the complex number.


It's like a vector where you are looking for the length of the vector.

the graph forms a right triangle with the x-axis as the adjacent side and the line parallel to the y-axis as the opposite side.


the hypotenuse is the vector and the length of that is found by the pythagorean formula of a^2 + b^2 = c^2 with a being the real part and b being the imaginary part.

Read the reference.  It explains it pretty well.