You may also like

problem icon

Thousand Words

Here the diagram says it all. Can you find the diagram?

problem icon

Complex Squares

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

problem icon

A Brief Introduction to the Argand Diagram

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

A Brief Introduction to Complex Numbers

Stage: 4 and 5 Challenge Level: Challenge Level:1
You are probably very familiar with $\mathbb{N}$, the set of natural numbers $1,2,3,4...$
The next set of numbers you met when you were younger might have been the integers, $\mathbb{Z}$, the positive and negative whole numbers.
You will also have met the rationals, $\mathbb{Q}$, numbers that can be written in the form $\frac{a}{b}$ where $a$ and $b$ are whole numbers which are coprime.
Finally, you will have come across irrational numbers such as $\sqrt2$ and $\pi$; these, together with the rationals, form the set of real numbers $\mathbb{R}$.

This problem introduces the set of complex numbers, $\mathbb{C}$

When you add together $2+2i$ and $3-i$, where does the real part of the answer come from? Where does the imaginary part of the answer come from?

What about when you multiply?