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Complex Squares

What happens when we square complex numbers? Can the square of a complex number be real?

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A Brief Introduction to Complex Numbers

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

A Brief Introduction to the Argand Diagram

Stage: 4 and 5 Challenge Level: Challenge Level:1

Pick a point for $z_1$ such as $2+i$. Move $z_2$ around, and keep a record of the points where $z_3$ is on the x-axis. What do you notice about the coordinates of $z_2$ and $z_3$?

Repeat for some other points.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.