## Visualizing a complex number

Just as a real number can be visualized on the number line, a complex number can be visualized on the complex plane in which the horizontal axis is the real axis and the vertical axis the imaginary axis.

Let $$z = -2+i$$ and $$w = 1+2i$$. They can be plotted on the complex plane as follows: The dotted yellow line represents all the complex numbers having real part equal to $$-2$$ and the dotted blue line represents all the complex numbers having imaginary part equal to $$1$$. Therefore, the intersection of these two lines represent the complex number with real part equal to $$-2$$ and imaginary part equal to $$1$$, which is the complex number $$z$$.

In general, a vertical line that crosses the real axis at the value $$a$$ represents all the complex numbers with real part equal to $$a$$. A horizontal line that crosses the imaginary axis at the value $$b$$ represents all the complex numbers with imaginary part equal to $$b$$.

## Rectangular form

A complex number written in the form $$a+bi$$ where $$a$$ and $$b$$ are real numbers is said to be in rectangular form (or standard form). But as we will see, the rectangular form is not the only way to specify a complex number.

## Exercises

Plot each of the following on the complex plane.

1. $$3$$

2. $$3+4i$$

3. $$3-4i$$

4. $$\displaystyle-2+\sqrt{3}i$$

5. $$2i$$