Complex Analysis Functions Complex Variable Online Exam Quiz
Complex Analysis Functions Complex Variable GK Quiz. Question and Answers related to Complex Analysis Functions Complex Variable. MCQ (Multiple Choice Questions with answers about Complex Analysis Functions Complex Variable
Let x, y, z be integers, not all simultaneously equal. If ? is a cube root of unity with Im(?)?1, and if f(z)=az2+bz+c, then find the range of |f(?)|.
Options
A : (0, ?)
B : [1, ?)
C : (?3/2, ?)
D : [1/2, ?)
Find the range of the function defined by f(z)=Re[2iz/(1-z2)].
Options
A : (??, 0) ? (0, ?)
B : [2, ?)
C : (??, ?1] ? [1, ?)
D : (??, 0] ? [2, ?)
For all complex numbers z satisfying Im(z)?0, if f(z)=z2+z+1 is a real valued function, then find its range.
Options
A : (-?, -1]
B : (-?, 1/3)
C : (-?, 1/2]
D : (-?, 3/4)
Let f(z)=arg 1/(1 – z), then find the range of f(z) for |z|=1, z?1.
Options
A : (-?, ?/2)
B : (-?/2, ?/2)
C : (-?, ?)
D : [0, ?/2)
Let f(z)=z+1/z. What will be the definition of this function in polar form?
Options
A : (r+1/r)cos?+i(r-1/r)sin?
B : (r-1/r)cos?+i(r+1/r)sin?
C : (r+1/r)sin?+i(r-1/r)cos?
D : (r+1/r)sin?+i(r-1/r)cos?
Define f(z)=z2+bz?1=0 and g(z)=z2+z+b=0. If there exists ? satisfying f(?)=g(?)=0, which of the following cannot be a value of b?
Options
A : ?3i
B : -?3i
C : 0
D : ?3i/2
Let f(z)=z4+a1z3+a2z2+a3z+a4=0; a1, a2, a3, a4 being real and non-zero. If f has a purely imaginary root, then what is the value of the expression a3/(a1a2)+ a1a4/(a2a3) ?
Options
A : 0
B : 1
C : -2
D : 2
Let f(z)=|z|2+Re z(2(z+z?)+3(z-z?)/2i, the find the maximum value of |z|2/f(z).
Options
A : 1
B : 2
C : 3
D : 4
Let f(z)=2(z+z?)+3i(z-z?) and g(z)=|z|. f(z)=2 divides the region g(z)?6 into two parts. If Q={(2+3i/4), (5/2+3i/4), (1/4-i/4), (1/8+i/4)}, then find the number of elements of Q lying inside the smaller part.
Options
A : 1
B : 2
C : 3
D : 4
Let f(z)=|1–z|, if zk=cos(2k?/10)+isin(2k?/10), then find the value of f(z1)×f(z2)×…×f(z9).
Options
A : 10
B : 15
C : 20
D : 30
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