Recent questions and answers in Complex Variables - GO Electrical

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GATE2013-23
Square roots of $-i$,where $i=\sqrt{-1}$, are $i,-i$ $\cos(-\frac{\pi }{4} )+i\sin(-\frac{\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$ $\cos(\frac{\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{\pi }{4})$ $\cos(\frac{3\pi }{4} )+i\sin(-\frac{3\pi }{4})+\cos(-\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$

asked Feb 12, 2017 in Complex Variables by piyag476 (1.5k points)

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GATE2014-2-4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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GATE2014-1-5
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$ where $z^{\ast}$ denotes the complex conjugate of $z$. The ... of the following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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4

GATE2015-2-1
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable at $z_{0}$ ... at $z_{0}$, then it is differentiable at $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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