Finding |3+4i|

Complex Analysis · Axiom Academy

EXAMPLE Finding the Modulus of 3 + 4i Use the Pythagorean theorem to find the modulus (absolute value) of a complex number. Find the modulus (absolute value) of the complex number z = 3 + 4i . In other words, compute |3 + 4i| . Nice work! You found the modulus of a complex number by treating it as a distance in the complex plane. The formula: For z = a + bi , the modulus is — the Pythagorean distance from the origin. Pythagorean triples: 3, 4, 5 form a triple ( 3^2 + 4^2 = 5^2 ). Spotting triples like (5, 12, 13) or (8, 15, 17) lets you find the modulus without a calculator. The modulus is just the length of the arrow from 0 to the point — a right-triangle hypotenuse in disguise.

This is the written version of the interactive lesson above. See the full Complex Analysis course.