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GATE201323
Square roots of $i$,where $i=\sqrt{1}$, are $i,i$ $\cos(\frac{\pi }{4} )+i\sin(\frac{\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$ $\cos(\frac{\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{\pi }{4})$ $\cos(\frac{3\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$
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Feb 12, 2017
in
Complex Variables
by
piyag476
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1.5k
points)
gate2013ee
complexnumber
trigonometry
0
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2
GATE201424
All the values of the multivalued complex function $1^i$,where $i=\sqrt{1}$ are purely imaginary. real and nonnegative on the unit circle. equal in real and imaginary parts.
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Feb 12, 2017
in
Complex Variables
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makhdoom ghaya
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9.3k
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gate2014ee2
imaginary
complexfunctions
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3
GATE201415
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
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Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
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9.3k
points)
gate2014ee1
complexconjugate
complexvariables
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4
GATE201521
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
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9.3k
points)
gate2015ee2
complexvaluedfunctions
complexvariable
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