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1.6aFree

How far is 3 + 4i from zero?

Your guide: Sir AhmedSays brackets have saved more marks than any calculator.

The problem

A complex number a + bi sits at the point (a, b) on the plane. But an address is not the whole story — every point also has a distance from home, from the origin.

Walk 3 blocks east and 4 blocks north, and the straight-line way home is a diagonal of 5 blocks, not 7. That diagonal is exactly what finding this distance means: Pythagoras, hiding in plain sight.

On the complex plane (Argand diagram), the x-axis is the real axis and the y-axis is the imaginary axis. The modulus |z| = |a + bi| = √(a2 + b2) is the distance from the origin to the point (a, b).

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