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Algebra - Complex Numbers Leaving Cert Helpdesk 27 th September 2012
Why do we need Complex Numbers?
Where are Complex Numbers used? Electronic Engineering Aircraft Design Medicine Movie/Computer game graphics
Adding and Subtracting Complex Numbers Group the real parts together and group the imaginary parts together. Examples:
Multiplication of Complex Numbers
Examples of Multiplication
The Complex Conjugate
Example of Division
Dividing one Complex Number by Another
Examples of the use of Complex Numbers
Modulus of a Complex Number
Polar Form of a Complex Number
Converting a Complex Number to Polar Form
De Moivres Theorem
De Moivres Theorem – Ex. 1
De Moivres Theorem - Example 2
Roots of a Complex Number
Proof by Induction
Proving De Moivres Theorem by Induction
PROGRAMME 2 COMPLEX NUMBERS 2.
Complex Numbers If we wish to work with , we need to extend the set of real numbers Definitions i is a number such that i2 = -1 C is the set of.
Section 1.4 Complex Numbers
Prepared by Dr. Taha MAhdy
2.4 Complex Numbers What is an imaginary number What is a complex number How to add complex numbers How to subtract complex numbers How to multiply complex.
Operations with Complex Numbers
Complex numbers Definitions Conversions Arithmetic Hyperbolic Functions.
Complex Numbers. Allow us to solve equations with a negative root NB: these are complex conjugates usually notated as z and z.
1.4. i= -1 i 2 = -1 a+b i Real Imaginary part part.
Complex Numbers Ideas from Further Pure 1 What complex numbers are The idea of real and imaginary parts –if z = 4 + 5j, Re(z) = 4, Im(z) = 5 How to add,
Complex Numbers S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Math Review with Matlab: Complex Math.
Polynomials Review and Complex numbers Newport Math Club Warm Up Problem: The game of assassin is played with 8 people and goes as follows: 1.Each player.
2.2 Complex Numbers Fri Feb 20 Do Now 1) 2x^2 -8 = 0 2) (sinx)^2 – 2sinx + 1 = 0.
6.2 – Simplified Form for Radicals
Complex Numbers i.
Section 5.4 Imaginary and Complex Numbers
Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.
Let’s do some Further Maths
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.
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