Answer:
2√37
Step-by-step explanation:
Given some complex number z, |z| is what's called magnitude of a complex number -- its distance from 0. Unlike the more straightforward process of finding the absolute value of a real number (a number on the number line) complex numbers are two-dimensional, and so to talk about their magnitude, we need to bring in the Pythagorean theorem.
The real and imaginary part of the complex number 12 - 2i represent the point (12, -2) on the complex plane. Drawing lines perpendicular to the real and imaginary axes and joining them with a line from the origin to the point gives us a right triangle with legs 12 and 2. Using the Pythagorean theorem, the hypotenuse, |12 - 2i|, must be equal to [tex]\sqrt{12^2+2^2}=\sqrt{148}[/tex]. We can pull a 4 out of the 148 to give us
[tex]\sqrt{4\cdot37}=\sqrt{4}\sqrt{37}=2\sqrt{37}[/tex]
