A square root of a number is a number whose square is . In other words, it is a solution to the equation . Every positive real number has two real square roots. For example, the number 35 has both  and  as square roots because those are the two numbers that square to make 35 (remember, the symbol together with a positive number is defined to indicate the positive square root). In other words, and .

Similarly, every negative real number has two imaginary square roots. The two square roots of -1 are written and . That means that and .

The two square roots of -17 are and , because

In general, if is a positive real number, then the square roots of are and .

Rarely, we might see something like . By convention, is defined to indicate the square root on the positive imaginary axis, so .

In this context, people call the real number line the real axis and the imaginary number line the imaginary axis. This is different than the coordinate plane that you have seen before because those points were pairs of real numbers, like , but in the complex plane, each point represents a single complex number. Note that since the real number line is part of the complex plane, real numbers are a special type of complex number. For example, the real number 5 can be described as the point in the complex plane.