Converting Complex Numbers

Pre-Calculus · Axiom Academy

EXAMPLE Converting Complex Numbers Work through rectangular polar conversions and a polar-form product, one decision at a time. We'll convert between the two forms of a complex number, then use polar form to multiply. Recall , , and . Nice work — you converted both directions and used polar form to multiply. Rectangular → polar: and — always check the quadrant to keep correct. Polar → rectangular: and ; the signs of a,b should match the quadrant of . Multiplying is easier in polar form: — multiply the magnitudes, add the angles. Rectangular form is built for adding and subtracting; polar form is built for multiplying, dividing, and powers. Knowing how to switch lets you pick the easier tool for any job.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.