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Trigonometric Form of Complex Numbers Summary of U4 L2 I1
2 Graphical Representation of a Complex Number Graph in coordinate plane Called the complex plane Horizontal axis is the real axis Vertical axis is the imaginary axis 3 + 4i -2 + 3i -5i
3 Absolute Value of a Complex Number Defined as the length of the line segment From the origin To the point Calculated by using Pythagorean Theorem 3 + 4i
4 Find That Value, Absolutely Try these Graph the complex number Find the absolute value
5 Trig Form of Complex Number Consider the graphical representation We note that a right triangle is formed a + bi θ b a r How do we determine θ?
6 Trig Form of Complex Number Now we use and substitute into z = a + bi Result is Abbreviation is often
7 Try It Out Given the complex number -5 + 6i Write in trigonometric form r = ? θ = ? Given z = 3 cis 315° Write in standanrd form r = ? a = ? b = ?
8 Product of Complex Numbers in Trig Form Given It can be shown that the product is Multiply the absolute values Add the θ's
9 Quotient of Complex Numbers in Trig Form Given It can be shown that the quotient is
10 Try It Out Try the following operations using trig form Convert answers to standard form
Chapter 6 Additional Topics in Trigonometry Trig Form of a Complex Number Objectives: Find absolute values of complex numbers. Write trig forms.
GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS A Complex Number is in the form: z = a+bi We can graph complex numbers on the axis shown below: Real axis.
Lesson 6.5 Trigonometric Form of Complex Numbers.
6.5 Complex Numbers in Polar Form. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 Objectives: Plot complex number in the complex plane. Find the.
11.2a Geometric Representation of a Complex Number Write complex numbers in polar form.
Trig form of Complex Numbers Objective: Be able to operate with complex numbers, and be able to convert complex numbers into Trig Form and vise versa.
Laws of Sines and Cosines Sections 8.1 and 8.2. Objectives Apply the law of sines to determine the lengths of side and measures of angle of a triangle.
Sec. 6.6b. One reason for writing complex numbers in trigonometric form is the convenience for multiplying and dividing: T The product i i i involves.
Write the expression as a complex number in standard form. 1.) (9 + 8i) + (8 – 9i) 2.) (-1 + i) – (7 – 5i) 3.) (8 – 5i) – ( i) Warm Up.
Copyright © 2007 Pearson Education, Inc. Slide Trigonometric (Polar) Form of Complex Numbers The Complex Plane and Vector Representations Call.
Copyright © 2011 Pearson Education, Inc. Slide Trigonometric (Polar) Form of Complex Numbers The Complex Plane and Vector Representations Call.
Graphing Complex Numbers AND Finding the Absolute Value of Complex Numbers SPI Compute with all real and complex numbers. Checks for Understanding.
Copyright © 2009 Pearson Education, Inc. CHAPTER 8: Applications of Trigonometry 8.1The Law of Sines 8.2The Law of Cosines 8.3Complex Numbers: Trigonometric.
Complex Numbers. Complex number is a number in the form z = a+bi, where a and b are real numbers and i is imaginary. Here a is the real part and b is.
Copyright © 2009 Pearson Addison-Wesley Complex Numbers, Polar Equations, and Parametric Equations.
Copyright © Cengage Learning. All rights reserved. 6.5 Trigonometric Form of a Complex Number.
5.4 – Complex Numbers. What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number. Imaginary numbers.
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 8 Complex Numbers, Polar Equations, and Parametric Equations.
Copyright © Cengage Learning. All rights reserved. 6 Additional Topics in Trigonometry.
Section 4.8 – Complex Numbers Students will be able to: To identify, graph, and perform operations with complex numbers To find complex number solutions.
1) Trig form of a Complex # 2) Multiplying, Dividing, and powers (DeMoivre’s Theorem) of Complex #s 3) Roots of Complex #s Section 6-5 Day 1, 2 &3.
Chapter Operations with complex numbers. Complex Plane O Just as you can represent real numbers graphically as points on a number line, you can.
Trigonometric Form of Complex Numbers. Real Axis Imaginary Axis Remember a complex number has a real part and an imaginary part. These are used to plot.
Copyright © 2009 Pearson Addison-Wesley Applications of Trigonometry.
The Distance Formula Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop.
8.2 Trigonometric (Polar) Form of Complex Numbers.
Holt Algebra Operations with Complex Numbers 5-9 Operations with Complex Numbers Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation.
Lesson 78 – Polar Form of Complex Numbers HL2 Math - Santowski 11/16/15.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Holt McDougal Algebra Operations with Complex Numbers Warm Up Express each number in terms of i Find each complex conjugate Find each.
Copyright © 2011 Pearson Education, Inc. Trigonometric Form of Complex Numbers Section 6.2 Complex Numbers, Polar Coordinates, and Parametric Equations.
Standardized Test Practice EXAMPLE 2 SOLUTION Plot points P, Q, R, and S on a coordinate plane. Point P is located in Quadrant IV. Point Q is located in.
Holt McDougal Algebra 2 Operations with Complex Numbers Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Trigonometric Form of a Complex Number Plot complex numbers in the complex plane and find absolute values of complex numbers. Write the trigonometric.
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1 of 10© Boardworks 2014 Group and Project Work. 2 of 10© Boardworks 2014 Information.
Aim: Complex & Imaginary Numbers Course: Adv. Alg. & Trig. Aim: What are imaginary and complex numbers? Do Now: Solve for x: x = 0 ? What number.
8.5 Polar Coordinates The rectangular coordinate system (x/y axis) works in 2 dimensions with each point having exactly one representation. A polar coordinate.
What are imaginary and complex numbers? Do Now: Solve for x: x = 0 ? What number when multiplied by itself gives us a negative one? No such real.
Slide 6-1 COMPLEX NUMBERS AND POLAR COORDINATES 8.1 Complex Numbers 8.2 Trigonometric Form for Complex Numbers Chapter 8.
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Geometry Ch 1-7 Midpoint and distance formulas
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers,
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Trigonometric Form of a Complex Number Digital Lesson.
5.6 – Complex Numbers. What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number. Imaginary numbers.
5-6 Complex Numbers Algebra 2 Prentice Hall, 2007.
8.4 – Trigonometric Form of Complex Numbers. From a while back, we defined a complex number as a number that may be written as… – z = a + bi – a is the.
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