Explore topic-wise MCQs in Complex Analysis.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Complex Analysis knowledge and support exam preparation. Choose a topic below to get started.

Explore topic-wise MCQs in Complex Analysis.

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) ?

For a∈R, let f(z)=z5-5z+a. Select the correct statement for α satisfying f(α)=0.

Let f(z)=|1–z|, if zk=cos(2kπ/10)+isin(2kπ/10), then find the value of f(z1)×f(z2)×…×f(z9).

Consider a function f(z) of degree two, having real coefficients. If z1 and z2 satisfying f(z1)=f(z2)=0 are such that Re z1=Re z2=0 and if z3 satisfies f(f(z3))=0, then select the correct statement.

Let f(z)=|z|2+Re z(2(z+z̅)+3(z-z̅)/2i, the find the maximum value of |z|2/f(z).

Find the range of the function defined by f(z)=Re[2iz/(1-z2)].

Let f(z)=2(z+z̅)+3i(z-z̅) 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.

Define f(z)=z2+bz−1=0 and g(z)=z2+z+b=0. If there exists α satisfying f(α)=g(α)=0, which of the following cannot be a value of b?

Let f(z)=arg 1/(1 – z), then find the range of f(z) for |z|=1, z≠1.

Let x, y, z be integers, not all simultaneously equal. If ω is a cube root of unity with Im(ω)≠1, and if f(z)=az2+bz+c, then find the range of |f(ω)|.

For all complex numbers z satisfying Im(z)≠0, if f(z)=z2+z+1 is a real valued function, then find its range.

Let f(z)=(z2–z–1)7. If α2+α+1=0 and Im(α)>0, then find f(α).

For the function f(z)=zi, what is the value of |f(ω)|+Arg f(ω), ω being the cube root of unity with Im(ω)>0?

Let f(z)=z+1/z. What will be the definition of this function in polar form?

Find the domain of the function defined by f(z)=z/(z+z̅).

Explore topic-wise MCQs in Complex Analysis.

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) ?

For a∈R, let f(z)=z5-5z+a. Select the correct statement for α satisfying f(α)=0.

Let f(z)=&vert;1–z&vert;, if zk=cos(2kπ/10)+isin(2kπ/10), then find the value of f(z1)×f(z2)×…×f(z9).

Consider a function f(z) of degree two, having real coefficients. If z1 and z2 satisfying f(z1)=f(z2)=0 are such that Re z1=Re z2=0 and if z3 satisfies f(f(z3))=0, then select the correct statement.

Let f(z)=&vert;z&vert;2+Re z(2(z+z̅)+3(z-z̅)/2i, the find the maximum value of &vert;z&vert;2/f(z).

Find the range of the function defined by f(z)=Re[2iz/(1-z2)].

Let f(z)=2(z+z̅)+3i(z-z̅) and g(z)=&vert;z&vert;. 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.

Define f(z)=z2+bz−1=0 and g(z)=z2+z+b=0. If there exists α satisfying f(α)=g(α)=0, which of the following cannot be a value of b?

Let f(z)=arg 1/(1 – z), then find the range of f(z) for &vert;z&vert;=1, z≠1.

Let x, y, z be integers, not all simultaneously equal. If ω is a cube root of unity with Im(ω)≠1, and if f(z)=az2+bz+c, then find the range of &vert;f(ω)&vert;.

For all complex numbers z satisfying Im(z)≠0, if f(z)=z2+z+1 is a real valued function, then find its range.

Let f(z)=(z2–z–1)7. If α2+α+1=0 and Im(α)>0, then find f(α).

For the function f(z)=zi, what is the value of &vert;f(ω)&vert;+Arg f(ω), ω being the cube root of unity with Im(ω)>0?

Let f(z)=z+1/z. What will be the definition of this function in polar form?

Find the domain of the function defined by f(z)=z/(z+z̅).

Let f(z)=|1–z|, if zk=cos(2kπ/10)+isin(2kπ/10), then find the value of f(z1)×f(z2)×…×f(z9).

Let f(z)=|z|2+Re z(2(z+z̅)+3(z-z̅)/2i, the find the maximum value of |z|2/f(z).

Let f(z)=2(z+z̅)+3i(z-z̅) 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.

Let f(z)=arg 1/(1 – z), then find the range of f(z) for |z|=1, z≠1.

Let x, y, z be integers, not all simultaneously equal. If ω is a cube root of unity with Im(ω)≠1, and if f(z)=az2+bz+c, then find the range of |f(ω)|.

For the function f(z)=zi, what is the value of |f(ω)|+Arg f(ω), ω being the cube root of unity with Im(ω)>0?