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?

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?