Skip over navigation
What do you get if you square $a+ib$?
Working backwards:
if $(a+ib)^2$ is real, what relationships must $a$ and $b$ satisfy?
if $(a+ib)^2$ is imaginary, what relationships must $a$ and $b$ satisfy?
What does this look like on an Argand diagram?
Complex Squares
Age 16 to 18
Challenge Level 
What do you get if you square $a+ib$?
Working backwards:
if $(a+ib)^2$ is real, what relationships must $a$ and $b$ satisfy?
if $(a+ib)^2$ is imaginary, what relationships must $a$ and $b$ satisfy?
What does this look like on an Argand diagram?
You may also like
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
Complex numbers can be represented graphically using an Argand diagram. This problem explains more...