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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 Imaginary Axis
ABSOLUTE VALUE OF A COMPLEX NUMBER An arrow is drawn from the origin to represent the complex number. The length of the arrow is the absolute value of the complex number.
REPRESENTING COMPLEX NUMBERS USING RECTANGULAR VS. POLAR COORDINATES So, We abbreviate this as cis
Complex Numbers Rectangular Form: Polar Form:
Example: Convert to rectangular form. Formulas:
Example: Convert to polar form. Formulas:
Example: What is the absolute value of the following complex numbers:
Do you want to go thru that every time? No!
SUMMARY To convert a+bi to polar: To convert to rectangular: Formulas: Formulas:
11.2a Geometric Representation of a Complex Number Write complex numbers in polar form.
Trigonometric Form of Complex Numbers
11.2 Geometric Representations 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.
9.7 PRODUCTS AND QUOTIENTS OF COMPLEX NUMBERS IN POLAR FORM By the end of this section students will be able to multiply and divide complex numbers in.
DeMoivre’s Theorem The Complex Plane. Complex Number A complex number z = x + yi can be interpreted geometrically as the point (x, y) in the complex plane.
Graphing Complex Numbers AND Finding the Absolute Value of Complex Numbers SPI Compute with all real and complex numbers. Checks for Understanding.
8.2 Trigonometric (Polar) Form of Complex Numbers.
Pre-Calculus Chapter 6 Additional Topics in Trigonometry.
10.3 Polar Form of Complex Numbers. We have explored complex numbers as solutions. Now we connect to both the rectangular and polar planes. Every complex.
11.2 GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS Can be confusing, polar form has a degree with it, rectangular form does not, this all takes place in.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
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.
The imaginary unit i is defined as Furthermore.
Copyright © 2009 Pearson Education, Inc. CHAPTER 8: Applications of Trigonometry 8.1The Law of Sines 8.2The Law of Cosines 8.3Complex Numbers: Trigonometric.
5-9 Operations with Complex Numbers Warm Up Lesson Presentation
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 8 Complex Numbers, Polar Equations, and Parametric Equations.
Complex Numbers in Polar Form; DeMoivre’s Theorem 6.5
Complex Numbers. a + bi Is a result of adding together or combining a real number and an imaginary number a is the real part of the complex number. bi.
Complex Numbers in Polar Form; DeMoivre’s Theorem
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