Q.No:1 JAM-2015
The phase of the complex number \((1+i)i\) in the polar representation is
(A)
\(\pi/4\)
(B)
\(\pi/2\)
(C)
\(3\pi/4\)
(D)
\(5\pi/4\)
Check Answer
Option C
Q.No:2 JAM-2016
Which one of the following points represent the complex number \(\frac{1}{1-i}\) ?
Check Answer
Option A
Q.No:3 JAM-2019
The value of \(|\int\limits_{0}^ {3+i}(\bar{z})^2 dz|^2\), along the line \(3y=x\), where \(z=x+iy\) is _____________.
(Round off to 1 decimal place)
Check Answer
Ans 111.0-111.2
Q.No:4 JAM-2021
One of the roots of the equation, \(z^6-3z^4-16=0\) is given by \(z_1=2\). The value of the product of the other five roots is _____________.
Check Answer
Ans (-8)
Q.No:5 JAM-2022
The equation \(z^2+\bar{z}^2=4\) in the complex plane (where \(\bar{z}\) is the complex conjugate of \(z\)) represents
(A)
Ellipse
(B)
Hyperbola
(C)
Circle of radius 2
(D)
Circle of radius 4
Check Answer
Option B
Q.No:6 JAM-2022
Consider a unit circle \(C\) in the \(xy\) plane, centered at the origin. The value of the integral \(\oint[(sin \hspace{1mm} x-y)dx- (sin \hspace{1mm} - x)dy]\) over the circle \(C\), traversed anticlockwise, is
(A)
0
(B)
\(2\pi\)
(C)
\(3\pi\)
(D)
\(4\pi\)
Check Answer
Option B
Q.No:7 JAM-2023
The roots of the polynomial, \( f(z) = z^4 - 8z^3 + 27z^2 - 38z + 26 \), are \(z_1\), \(z_2\), \(z_3\), \& \(z_4\), where \(z\) is a complex variable. Which of the following statements is correct?
A) \(\frac{z_1 + z_2 + z_3 + z_4}{z_1z_2z_3z_4} = -\frac{4}{19}\)
B) \(\frac{z_1 + z_2 + z_3 + z_4}{z_1z_2z_3z_4} = \frac{4}{13}\)
C) \(\frac{z_1z_2z_3z_4}{z_1 + z_2 + z_3 + z_4} = -\frac{26}{27}\)
D) \(\frac{z_1z_2z_3z_4}{z_1 + z_2 + z_3 + z_4} = \frac{13}{19}\)