Exercises: Represent Operations Geometrically on the Complex Plane

Show your work. Use exact values where possible. For polar form, express angles in degrees.

Grade 9·22 problems·~40 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-b-5

Work through problems with immediate feedback

Fluency Practice

Start with the complex number $1 + 0i$ (at angle $0°$ and modulus $1$ ). Multiply by $i$ once. Where does the result land on the complex plane?

$-1 + 0i$ — on the negative real axis ($180°$)

$0 + i$ — on the positive imaginary axis ($90°$)

$0 - i$ — on the negative imaginary axis ($270°$)

$1 + i$ — in the first quadrant ($45°$)