Add “like terms” in the expression . What do you get?
Write these sums and differences in the form , where and are real numbers.
(Check your work by drawing a diagram.)
9.3
Activity
Draw points to represent 2, 22, 23, and 24 on the real number line. What do you notice about the arrangement of the points?
Write , , , and in the form .
Plot , , , and on the complex plane. What do you notice about the arrangement of the points?
Student Lesson Summary
When we add a real number with an imaginary number, we get a complex number. We usually write complex numbers as:
where and are real numbers. We say that is the “real part” and is the “imaginary part.”
To add (or subtract) two complex numbers, we add (or subtract) the real parts and add (or subtract) the imaginary parts. For example:
In general:
and:
When we raise an imaginary number to a power, we can use the fact that to write the result in the form . For example, . We can group the factors together to see how to rewrite this.
