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Recent questions tagged complex-number

2 votes
1 answer
3
ISI2015-MMA-18
The set of complex numbers $z$ satisfying the equation $(3+7i)z+(10-2i)\overline{z}+100=0$ represents, in the complex plane, a straight line a pair of intersecting straight lines a point a pair of distinct parallel straight lines
The set of complex numbers $z$ satisfying the equation $$(3+7i)z+(10-2i)\overline{z}+100=0$$ represents, in the complex plane,a straight linea pair of intersecting straig...
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1 votes
1 answer
4
ISI2015-MMA-21
Let $\omega$ denote a complex fifth root of unity. Define $b_k =\sum_{j=0}^{4} j \omega^{-kj},$ for $0 \leq k \leq 4$. Then $ \sum_{k=0}^{4} b_k \omega ^k$ is equal to $5$ $5 \omega$ $5(1+\omega)$ $0$
Let $\omega$ denote a complex fifth root of unity. Define $$b_k =\sum_{j=0}^{4} j \omega^{-kj},$$ for $0 \leq k \leq 4$. Then $ \sum_{k=0}^{4} b_k \omega ^k$ is equal to$...
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0 votes
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5
ISI2015-MMA-83
If $\alpha, \beta$ are complex numbers then the maximum value of $\dfrac{\alpha \overline{\beta}+\overline{\alpha}\beta}{\mid \alpha \beta \mid}$ is $2$ $1$ the expression may not always be a real number and hence maximum does not make sense none of the above
If $\alpha, \beta$ are complex numbers then the maximum value of $\dfrac{\alpha \overline{\beta}+\overline{\alpha}\beta}{\mid \alpha \beta \mid}$ is$2$$1$the expression m...
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1 votes
1 answer
7
NIELIT 2018-28
For the function $(z) = \frac{1}{z^2(e^z-1)}, z=0$ is a pole of order: $1$ $2$ $3$ None of these
For the function $(z) = \frac{1}{z^2(e^z-1)}, z=0$ is a pole of order:$1$$2$$3$None of these
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0 votes
1 answer
8
ISI2016-MMA-2
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$? $0$ $1$ $2$ $3$
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$?$0$$1$$2$$3$
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0 votes
1 answer
9
Syllabus Gate 2019
Is the chapter Complex functions part of gate 2019 maths syllabus? Previously questions about analytic functions have been asked a lot. Are they part of the syllabus?
Is the chapter Complex functions part of gate 2019 maths syllabus?Previously questions about analytic functions have been asked a lot. Are they part of the syllabus?
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1 votes
1 answer
10
ISI MMA QROR
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n } Then lim n→∞ Gn is
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n }Then lim n→∞ Gn is
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1 votes
3 answers
11
ISI-2016-02
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ? $0$ $1$ $2$ $3$
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ?$0$$1$$2$$3$
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0 votes
0 answers
12
ISI-2014-17
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$? $0$ $1$ $2$ $3$
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$?$0$$1$$2$$3$
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0 votes
1 answer
13
ISI-2014-3
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true $Re(z)=0$ $\mid z \mid =1$ $Re(z) = 1$ $\text{No such z exists}$
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true$Re(z)=0$$\mid z \mid =1$$Re(z) = 1$$\text{No such z exists}$
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1 votes
0 answers
14
Complex number
The real values of $(a+ib)^{\dfrac{1}{n}} + (a-ib)^{\dfrac{1}{n}}$ is
The real values of $(a+ib)^{\dfrac{1}{n}} + (a-ib)^{\dfrac{1}{n}}$ is
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1 votes
0 answers
15
Mathematics GATE 2018 CH: 54
The deacy ratio for a system having complex conjugate poles as $(-\dfrac{1}{10} + j\dfrac{2}{15})$ and $(-\dfrac{1}{10} - j\dfrac{2}{15})$ is $7\times10^{-1}$ $8\times10^{-2}$ $9\times10^{-3}$ $10\times10^{-4}$
The deacy ratio for a system having complex conjugate poles as$(-\dfrac{1}{10} + j\dfrac{2}{15})$ and $(-\dfrac{1}{10} - j\dfrac{2}{15})$ is$7\times10^{-1}$$8\times10^{-2...
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0 votes
1 answer
16
Complex
Find the modulus and argument of $\frac{1+i}{7+24i}$
Find the modulus and argument of $$\frac{1+i}{7+24i}$$
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1 votes
2 answers
17
How to solve below equation ?
The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______. 1 0 -1 2
The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______.10-12
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2 votes
1 answer
18
TIFR CSE 2013 | Part A | Question: 7
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ ... $\frac{1}{3}$ 1 3 $\frac{1}{2}$
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ are three complex numbers w...
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8 votes
4 answers
19
TIFR CSE 2011 | Part A | Question: 13
If $z=\dfrac{\sqrt{3}-i}{2}$ and $\large(z^{95}+ i^{67})^{97}= z^{n}$, then the smallest value of $n$ is $1$ $10$ $11$ $12$ None of the above
If $z=\dfrac{\sqrt{3}-i}{2}$ and $\large(z^{95}+ i^{67})^{97}= z^{n}$, then the smallest value of $n$ is$1$$10$$11$$12$None of the above
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0 votes
1 answer
21
Value of a^2+b^2 ?
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