Complex Numbers

Complex Modulus

|z| = distance from origin

  • High school
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a = 3b = 4|z|=5.003+4i
a = 3
b = 4
∣z∣2=a2+b2=32+42=25|z|^2 = a^2 + b^2 = 3^2 + 4^2 = 25
∣z∣=25=5.0000|z| = \sqrt{25} = 5.0000

|z| is the distance from z to the origin. It's literally the Pythagorean theorem: real and imaginary parts form a right triangle, the modulus is the hypotenuse.