We have learnt previously that we cannot find the root of a negative number, but that is not entirely true. If we take the root of a negative number, we have what is known as an imaginary number (unreal number).
If we solve a quadratic equation and arrive at a solution as:
This is known as a complex number and consists of two parts - a real part (2) and an imaginary part (root of -4). A complex number is often designated as z.
The definition of the imaginary part is
How do you calculate the root of a negative number?
The solution to our quadratic equation in the beginning of the chapter is thus:
The two roots are very similar except for the sign preceding the imaginary number. Such numbers are known as conjugates of each other. You designate a conjugate with a dash above the symbol:
Calculating with complex numbers proceeds as in ordinary mathematics but you should remember that
Rewrite the given expression in the a+bi form: