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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
Topic 6 Topic 6 Real and Complex Number Systems II 9.1 – 9.5, 12.1 – 12.2 Algebraic representation of complex numbers including: Cartesian, trigonometric.
PROGRAMME 2 COMPLEX NUMBERS 2.
Trigonometric Form of a Complex Number
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
CIVE Engineering Mathematics 2.2
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
Advanced Precalculus Notes 8.3 The Complex Plane: De Moivre’s Theorem
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,
Know what is meant by proof by Induction Learning Outcomes: PROOF BY INDUCTION Be able to use proof by induction to prove statements.
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
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