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Recent questions tagged complex-number

1 vote
1 answer
1
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
asked Sep 23, 2019 in Numerical Ability Arjun 134 views
1 vote
1 answer
2
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 $5$ $5 \omega$ $5(1+\omega)$ $0$
asked Sep 23, 2019 in Others Arjun 97 views
0 votes
0 answers
3
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
asked Sep 23, 2019 in Others Arjun 51 views
0 votes
1 answer
4
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {-1}$. Then which ... $f$ is degenerate on $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$
asked May 7, 2019 in Others Sayan Bose 542 views
0 votes
1 answer
5
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$? $0$ $1$ $2$ $3$
asked Sep 13, 2018 in Others jothee 51 views
0 votes
1 answer
6
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?
asked Jul 3, 2018 in Mathematical Logic bts 328 views
1 vote
1 answer
7
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n } Then lim n→∞ Gn is
asked Apr 15, 2018 in Calculus Partha De 279 views
1 vote
3 answers
8
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ? $0$ $1$ $2$ $3$
asked Mar 30, 2018 in Mathematical Logic jjayantamahata 137 views
0 votes
0 answers
9
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$? $0$ $1$ $2$ $3$
asked Mar 18, 2018 in Mathematical Logic jjayantamahata 97 views
0 votes
1 answer
10
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true $Re(z)=0$ $\mid z \mid =1$ $Re(z) = 1$ $\text{No such z exists}$
asked Mar 17, 2018 in Mathematical Logic jjayantamahata 65 views
1 vote
0 answers
11
The real values of $(a+ib)^{\dfrac{1}{n}} + (a-ib)^{\dfrac{1}{n}}$ is
asked Feb 27, 2018 in Linear Algebra Niranjankrraj 241 views
1 vote
0 answers
12
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 $7\times10^{-1}$ $8\times10^{-2}$ $9\times10^{-3}$ $10\times10^{-4}$
asked Feb 20, 2018 in Calculus Lakshman Patel RJIT 194 views
2 votes
1 answer
13
Which of the following statements about the eigen values of $I_n$, the $n \times n$ identity matrix (over complex numbers), is true? The eigen values are $1, \omega, \omega^2, \dots , \omega^{n-1}$, where $\omega$ is a primitive $n$-th root of unity The only eigen value ... eigen values, but there are no other eigen values The eigen values are 1$, 1/2, 1/3, \dots , 1/n$ The only eigen value is 1
asked Dec 26, 2016 in Others jothee 138 views
0 votes
1 answer
14
Find the modulus and argument of $\frac{1+i}{7+24i}$
asked Jun 11, 2016 in Unknown Category Pragy Agarwal 249 views
1 vote
2 answers
15
The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______. 1 0 -1 2
asked Nov 18, 2015 in Calculus radha gogia 226 views
2 votes
0 answers
16
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 with the same modulus but different phases ($arg z_{3} < arg z_{2} < arg z_{1} < 180^{∘}$ ... $\frac{1}{3}$ 1 3 $\frac{1}{2}$
asked Nov 4, 2015 in Numerical Ability makhdoom ghaya 161 views
6 votes
2 answers
17
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.
asked Oct 19, 2015 in Numerical Ability makhdoom ghaya 403 views
3 votes
1 answer
18
Three distinct points $x, y, z$ lie on a unit circle of the complex plane and satisfy $x+y+z=0$. Then $x, y, z$ form the vertices of . An isosceles but not equilateral triangle. An equilateral triangle. A triangle of any shape. A triangle whose shape can't be determined. None of the above.
asked Oct 17, 2015 in Numerical Ability makhdoom ghaya 207 views
0 votes
1 answer
19
asked Mar 29, 2015 in Linear Algebra Proton 189 views
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