When we look at the expression, we see that there have been given sums, differences and products of the complex numbers. To add or subtract two complex numbers, we add or subtract their real parts and imaginary parts.
Sum and Difference of Complex Numbers(a+bi)±(c+di)=(a±c)+(b±d)i
When we multiply two complex numbers, we use and we have
i2 as a result of this operation. In this case, we should simplify
i2 as
-1. Keeping these in mind, let's simplify each of the corresponding expressions.
Given
|
Simplified
|
(-4+7i)+(-4−7i)
|
-8+0i
|
(2−6i)−(-10+4i)
|
12−10i
|
(25+15i)−(25−6i)
|
0+21i
|
(5+i)(8−i)
|
41+3i
|
(17−3i)+(-17−6i)
|
0−9i
|
(-1+2i)(11−i)
|
-9+23i
|
(7+5i)+(7−5i)
|
14+0i
|
(-3+6i)−(-3−8i)
|
0+14i
|
Now, the expressions are written in
standard form. A written in
standard form is a number
a+bi where
a and
b are real numbers. The number
a is the
real part, and the number
bi is the
imaginary part.
a+bi
Therefore, we have three cases.
- If b=0, then a+bi is an
- If b=0, then a+bi is a
- If a=0, then a+bi is a pure imaginary number.
With these, let's classify our results.
Real numbers
|
Imaginary numbers
|
Pure imaginary numbers
|
-8+0i14+0i
|
12−10i41+3i-9+23i
|
0+21i0−9i0+14i
|