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Definition of pure imaginary numbers:Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.
it is a symbol for a specific numberDefinition of pure imaginary numbers: i is not a variable it is a symbol for a specific number
Simplify each expression.
Simplify each expression.Remember Remember
Definition of Complex NumbersAny number in form a+bi, where a and b are real numbers and i is imaginary unit.
Definition of Equal Complex NumbersTwo complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d
When adding or subtracting complex numbers, combine like terms.
Solving quadratic functions with complex numbers.subtract 2 Take the square root of both sides simplify
Multiplying complex numbers.To multiply complex numbers, you use the same procedure as multiplying polynomials.
Simplify. F O I L
Simplify. F O I L
CONJUGATES Each imaginary unit has a conjugate. Two imaginary units are conjugates if and only if their products are a real number.
Dividing complex numbers.To divide complex numbers you must multiply the numerator and denominator by the conjugate of the denominator.
What’s the conjugate of the denominator?
Your turn. Write in standard form by dividing.
Graphing complex numbersy-axis is the imaginary axis. x-axis is the real numbers Identify the numbers plotted.
Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary. What is an imaginary number?
Complex Numbers Objectives Students will learn:
7.5 – Rationalizing the Denominator of Radicals Expressions
Complex Numbers Section 0.7. What if it isnt Real?? We have found the square root of a positive number like = 4, Previously when asked to find the square.
1.4. i= -1 i 2 = -1 a+b i Real Imaginary part part.
COMPLEX NUMBERS Objectives
6.2 – Simplified Form for Radicals
Objectives for Class 3 Add, Subtract, Multiply, and Divide Complex Numbers. Solve Quadratic Equations in the Complex Number System.
Review and Examples: 7.4 – Adding, Subtracting, Multiplying Radical Expressions.
Complex Numbers OBJECTIVES Use the imaginary unit i to write complex numbers Add, subtract, and multiply complex numbers Use quadratic formula to find.
Warm-upAnswers Compute (in terms of i) _i, -1, -i, 1.
Section 5.4 Imaginary and Complex Numbers
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
1.3 Complex Number System.
Notes Over 5.4 Imaginary Numbers.
Section 2-5 Complex Numbers.
Copyright © 2009 Pearson Addison-Wesley Complex Numbers, Polar Equations, and Parametric Equations.
Sullivan Algebra and Trigonometry: Section 1.3 Quadratic Equations in the Complex Number System Objectives Add, Subtract, Multiply, and Divide Complex.
5.6 Complex Numbers. Solve the following quadratic: x = 0 Is this quadratic factorable? What does its graph look like? But I thought that you could.
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