# Tagged Questions

Questions involving complex numbers, that is numbers of the form $a+bi$ where $i^2=-1$ and $a,b\in\mathbb{R}$.

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### Preposition about the Entries of the Product of Markov Matrices.

Definition: A Markov matrix is an $n \times n$ complex matrix with the sum of the elements in every column equal to 1. My task is to prove that: If A, B are Markov matrices such that $|a_{ij}|\leq1$ ...
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### Tangent and Circle in Complex Plane

Question:- Three points represented by the complex numbers $a,b$ and $c$ lie on a circle with center $O$ and radius $r$. The tangent at $c$ cuts the chord joining the points $a$ and $b$ at $z$. ...
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### On real part of the complex number $(1+i)z^2$

Find the set of points belonging to the coordinate plane $xy$, for which the real part of the complex number $(1+i)z^2$ is positive. My solution:- Lets start with letting $z=r\cdot e^{i\theta}$. ...
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### find the principal part of the function at its isolated singular point

find the principal part of the function at its isolated singular point, and determine whether that point is a pole, a removable singular point, or an essential singular point. (a) f(z) = z exp(1/z) (...