Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
2. Complex Numbers
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Exercise 65 Page 109

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
Practice makes perfect
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 Distributive Property and we have i^2 as a result of this operation. In this case, we should simplify i^2 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 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