BS Physics Notes Series

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Mathematical Methods in Physics
151 Analytic Functions of Complex Variables
152 Asymptotic Expansions
153 Change of Basis
154 Bessel Functions of first kind, Bessel Functions of the second kind, Modified Bessel Functions, Spherical
Bessel Functions
155 Beta Function

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Mathematical Methods in Physics
156 Cauchy’s Theorem
157 Cauchy-Goursat Theorem
158 Cauchy’s Integral Formulas
159 Cauchy–Riemann Equations
160 Chebyshev Polynomials
161 Christoffel symbols
Mathematical Methods in Physics
162 Complex Analysis, Polar form of complex numbers, Complex logarithms and powers
163 Complex Integration
164 Complex Numbers
165 Contour Integrals
166 Covariant Differentiation
167 Convolution Theorem
Complex Analysis
A number of the form a + ib, where a and b are real numbers, is called a complex number, a is called the
real part and b is called the imaginary part of the complex number.

90. 493
Addition of two complex numbers
Difference of two complex numbers

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Multiplication of two complex numbers

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The distributive law

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Division of two complex numbers
Power of i
We know that

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Prove
Proof:

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The Modulus and the Conjugate of a Complex Number
Example

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Solution
Let z = 2 – 3i
Example
Find the modulus and argument of the complex numbers:
Solution

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98. 501
Example
Solution

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Example
Solution
Example

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Solution
These are properties of the functions cos z and sin z:

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