Mymathware Shafii's Math Academy

Dumelang guys!!! In this post, we will explore the real and imaginary parts of the complex logarithm function \( w = \log{z} \), and show that they satisfy the Cauchy-Ri…

Sanbonani guys!!!  This is MMTC081 (Complex Analysis Module).  Here we look into some uncommon problems we have encountered in the course of studying this module.   (1) …

Lecture series by Dr Kamran Khan on Complex Integration Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim Universi…

The harmonic functions and construction of analytic functions.  In this video series Dr. Kamran Khan takes us through harmonic functions and construction of analytic fun…

Polar form of Cauchy-Riemann equations In this lecture series, Dr. Kamran Khan takes us through polar forms of Cauchy-Riemann equation, how they are derived and example…

Example of a function that satisfies the Cauchy-Riemann equation. In this lecture Dr. Kamran Khan takes his time to solve a problem that satisfies the Cauchy-Riemann equ…

Analytic functions and the Cauchy-Riemann equation - Lecture II In this lesson Professor Kamran Khan takes us through the Cauchy Riemann equation which is an equation th…

Introduction to complex analysis by Dr. Kamran Khan. Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim University, Aligarh India. Ka…

A short note on the Riemann sphere and some of its properties.  Bernhard Riemann's great contribution to mathematics led to the discovery of the Riemann sphere, the …

Enoch Opeyemi, the Nigeria professor who attempted a proof of the Riemann hypothesis. A photo of Enoch Opeyemi. During the third trimester of 2015, the Nigeria news medi…

What is a transcendental number, examples and properties? Happy new year to all my readers and followers. Today, i will be celebrating the new year with you by writing o…

Proving the Madhava-Leibniz series for pi(π)  One of the earliest known approximations of $\pi$ was done by an Indian mathematician Madhava of Sangamagrama during th…

Evaluate the complex number into real and imaginary parts $\sqrt{i}^\sqrt{i}$.  Solution From indices we know that $\sqrt{i}=i^\frac{1}{2}$ $i^\frac{1}{2}=[\cos\frac{\pi…

Solution to MAT306[Complex Analysis II] Test Below is a solution to questions of MAT306 complex analysis II test. The topics treated include contour integration, connec…

The Harmonic Functions The Harmonic functions is a Function That satisfy the Laplace equation.In order words the harmonic function is defined as:

Definition of Analytic Functions i) A complex function $f(z)$ is said at a point $z_0$, if $f$ is differentiable not only at $z_0$ but at every point of some neighborho…

We define a parameterized curve to be any function Z→[a,b]→C where c belongs to the set of  complex number. A parameterized curve is said to be a smooth curve if Z : [a…