IMAGINARY AND COMPLEX NUMBERS
Higher Concepts of Mathematics
Imaginary numbers are added or subtracted by writing them using the imaginary unit i and then
adding or subtracting the real number coefficients of i. They are added or subtracted like
algebraic terms in which the imaginary unit i is treated like a literal number. Thus,
are added by writing them as 5i and 3i and adding them like algebraic terms. The result is 8i
equals 3i subtracted
from 5i which equals 2i or
Combine the following imaginary numbers:
4i 6i 7i i
Thus, the result is 2i 2
Imaginary numbers are multiplied or divided by writing them using the imaginary unit i, and then
multiplying or dividing them like algebraic terms. However, there are several basic relationships
which must also be used to multiply or divide imaginary numbers.
i2 = (i)(i) =
1 ) (
i3 = (i2)(i) = (-1)(i) = -i
i4 = (i2)(i2) = (-1)(-1) = +1
Using these basic relationships, for example,
equals (5i)(2i) which equals 10i2.
But, i2 equals -1. Thus, 10i2 equals (10)(-1) which equals -10.
Any square root has two roots, i.e., a statement x2 = 25 is a quadratic and has roots
x = 5 since +52 = 25 and (-5) x (-5) = 25.