Complex Quest.
Plot complex numbers. Turn points into patterns. Make colourful loci with modulus and argument. Every mark is real mathematics.
Five ways to make an Argand masterpiece
Choose your maths, then reveal your artwork.
Your five pictures have independent progress on this device. No account needed. Already know complex numbers? Jump to any difficulty.
Star Trail
The Argand plane
Your proposed point or region is outlined until you check it. Only correct mathematical objects become artwork.
Plot the complex number
Plot z = 0 + 4i
Choose the correct point on the Argand plane.
Angles are measured anticlockwise from the positive real axis in radians.
Your proposal: 0
How does this challenge work?
Plot: Re(z) goes across, Im(z) goes up. Transform: conjugation reflects; multiplying by i rotates through 90° anticlockwise. Modulus: |z − c| is distance from c. Argument: arg(z − c) is the angle measured from c. A strict inequality has a dashed boundary.