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Solving Nonlinear Equations by Substitution
Solving Absolute Value Inequalities
Quadratic Equations
Real Numbers and Notation
The Distance Formula
Properties and Facts of Addition
Multiplying Complex Numbers
Factoring Trinomials by Grouping
Representing Simple Arithmetic Symbolically
Distributive Rule
Solving Equations by Factoring
Adding and Subtracting Mixed Fractions
Dividing Radicals
Circumference and Area of Circles
Quadratic Equations
Adding and Subtracting Polynomials
Multiplying Multiples of Numbers Together
Linear Equations
Dividing Fractions
Solving Linear Equations
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Adding Triangular Numbers
Rounding Numbers and Estimating Answers
Higher Degree Polynomial Functions
Rules for Arithmetic With Approximate Numbers
Combining Like Radical Terms
Zero Exponent
Proportions
Signs of Products or Quotients of Signed Numbers
Graphing Technology: Parent and Family Graphs
Using the
Solving Nonlinear Equations by Factoring
Graphing Linear Equations
Solving Systems of Equations by Graphing
Slope
Properties of Rational Expressions
Order of Operations
Solving Simple Equations
Powers of Complex Numbers
Factoring By Grouping
Solving Inequalities
Comparing Decimals
Absolute Value Function
Adding and Subtracting Rational Expressions
Multiplying and Dividing Fractions
Product and Quotient of Functions
Multiplication by 12
Negative Exponents and Scientific Notation
Slope
Division Property of Radicals
Special Products
Slope
Negative Exponents
Scientific Notation
The Distance Formula
Solving Systems of Linear Equations in Three Variables
Prime Numbers
Division and Factoring
Solving Equations Involving Rational Expressions
Simplifying Sums and Differences of Square Roots
Solving Linear Systems of Equations by Substitution
Powers of a Monomial
Solving Linear Equations
Solving Equations with Radicals and Exponents
Linear Relations and Functions
Complex Numbers
Simplifying Complex Fractions
Writing Algebraic Expressions
Absolute Value
Factoring General Polynomials
The Slope of a Line
Positive and Negative Slopes
Solving Linear Inequalities with Fractions
Solving Linear Inequalities
Writing Linear Equations in Slope-Intercept Form
Solving Quadratic Equations Using the Quadratic Formula
Solving Equations by Factoring
Factoring Trinomials
Equations Quadratic in Form
Negative Integral Exponents
Solving Equations with Variables on Each Side
Dividing a Polynomial by a Binomial
Synthetic Division
Combining Operations
Linear Equations
Powers
Multiplying Fractions
Dividing Monomials
Multiplication Property of Equality
Percents
Factoring Trinomials by Grouping
Dividing Complex Numbers
Solving Absolute Value Equations
Dividing Rational Expressions
Solving Quadratic Equations
Solving Systems of Equations By Addition (Elimination)
The Product and Quotient Rules
Linear Systems of Equations with No Solution
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations by Completing the Square
   
 

Multiplying Complex Numbers

Multiplying complex numbers is very much like multiplying polynomials. When we simplify the result, we replace each occurrence of i2 with -1. We often write the final result in the form a + bi.

 

Example 1

Find: 5i · 7i

Solution

Multiply 5 · 7 and multiply i · i.

Replace i2 with -1.

Multiply.

So, 5i · 7i = -35.

 5i · 7i

= 35 · i2

= 35 · (-1)

= -35

Note:

We write -35 in the form a + bi like this: 0 + (-35)i

 

Example 2

Find: 4i(9 - 6i)

Solution

Distribute 4i.

Multiply the factors in each term.

Replace i2 with -1.

Simplify.

Write the result in the form a + bi.

So, 4i(9 - 6i) = 24 + 36i.

   4i(9 - 6i)

= 4i · 9 - 4i · 6i

= 36i - 24i2

= 36i - 24(-1)

= 36i + 24

= 24 + 36i

 

Example 3

Find: (7 - 4i)(10 + 5i)

Solution

Multiply using the FOIL method.

Multiply the factors in each term.

Replace i2 with -1.

Combine like terms.

So, (7 - 4i)(10 + 5i) = 90 - 5i.

    (7 - 4i)(10 + 5i)

= 7 · 10 + 7 · 5i - 4i · 10 - 4i · 5i

= 70 + 35i - 40i - 20i2

= 70 + 35i - 40i - 20(-1)

= 70 + 35i - 40i + 20

= 90 - 5i
 
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