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Watch the video below to see how complex numbers can be defined.
If you can't see the video, reveal the hidden text which describes the video.
Choose some complex numbers of your own and practise adding, subtracting and multiplying them.
A real number is of the form $x+0i$. An imaginary number is of the form $0+iy$.
Here are some questions you might like to consider:
In general, what would you need to add to $a+ib$ to get a real number? Or an imaginary number?
In general, what would you need to multiply by $a+ib$ to get a real number? Or an imaginary number?
Now have a look at A Brief Introduction to the Argand Diagram.