2. Complex Numbers
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To add or subtract two complex numbers, we add or subtract their real parts and imaginary parts. You should also remember that when simplifying an expression that involves complex numbers, we should simplify i^2 as -1.
Real numbers | Imaginary numbers | Pure imaginary numbers |
---|---|---|
-8 14 | 12-10i 41+3i -9+23i | 21i -9i 14i |
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 complex number 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.
With these, let's classify our results.
Real numbers | Imaginary numbers | Pure imaginary numbers |
---|---|---|
-8+0i 14+0i | 12-10i 41+3i -9+23i | 0+21i 0-9i 0+14i |