Pure Mathematics: Complex numbers, Volume 3 |
Contents
Definition of a Complex Number 2 Plotting a Complex Numbers in an Argand Diagram | 1 |
The Sum and Difference of two Complex Numbers | 6 |
Determines the product of two Complex Numbers in the Quadratic form | 8 |
Defines the Conjugate of a Complex Number | 10 |
Determines the Quotient of two Complex Numbers | 12 |
Defines the Modulus and Argument of Complex Numbers | 14 |
Converts the Cartesian form x + yi into polar form 9 Multiplies and divides Comples Numbers using the polar form | 15 |
Determines the square roots of Complex Number | 24 |
15 | 34 |
18 | 36 |
Loci Expands cos no sin në and tan no where n is any positive integer 14 Application of De Moivres Theorem 16 18 Relates Hyperbolic and Trigono... | 39 |
Complex form of a circle and straight line | 54 |
Transformations from a ZPlane to a WPlane employing 6168 | 55 |
Miscellaneous 6973 | 61 |
22 | 64 |
Additional Examples with Solutions 7477 | 69 |
Proof of De Moivres Theorem by induction and otherwise | 26 |
3 | 28 |
8 | 30 |
10 | 31 |
14 | 32 |
Multiple choice questions | 74 |
Recapitulation or summary | 78 |
Answers | 79 |
| 86 | |
Common terms and phrases
added or subtracted angle anticlockwise direction arg Z arg Z2 arg(Z Argand diagram cartesian equation cartesian form circle with centre complex numbers Z1 cos2 cos² 0 sin² cos³ cosh cot2 cube roots cubic equation denominator Determine Equating real equation Z³ Example Exercises exponential form Find the complex Find the modulus following complex numbers GCE A level given hyperbolic functions imaginary terms integer Level ISBN-13 loci modulus and argument Moivre's theorem multiplying number Z OP₁ P₁ polar form polynomial equation positive x-axis prove quadratic equation quotient radius real and imaginary real coefficients real numbers represents the complex roots of unity sin³ sinh Solution square roots straight line sum and difference Transformation trigonometric functions viii W-plane Write y-axis Z₁ Z1 and Z2 Απ π π Зл