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MCQ on Complex Numbers
Questions compiled by Dr. Suvra Kanti Chakraborty, Assistant Professor, RKM Vidyamandira, Belur Math. Email:
suvra.maths@gmail.com
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Q. z=(a+bi)^{4n}+(b+ai)^{4n}, where a and b real numbers and n is natural number then z is
2 points
not necessarily real
complex where real part equals imaginary part
purely imaginary
real
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Q. If m and n are natural numbers and, then the equations z^n=1+i and z^m=2-i
2 points
have exactly one common solution
have infinitely many common solutions
have no common solution
have finitely many common solutions
Clear selection
Q. z=(1+i)/(1-i) and w=sqrt(2)/(1-i) then
2 points
|z|=2. |w|=1
|z|=|w|=1
|z|=|w|=2
|z|=1, |w|=2
Clear selection
Q. z=(2+3i)^{4n+2} + (3-2i)^{4n+2}, then z=
2 points
2
2i
0
3i
Clear selection
Q. solve: z-12=i(9-2 bar(z))
2 points
z=5+2i
z=2+5i
z=2+2i
z=5+5i
Clear selection
Q. The argument of the complex number (1+i)^4
2 points
pi/2
0
-pi/2
pi
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Q. If w is an imaginary cube root of unity, then (1 + w – w^2)^7 is equal to
2 points
-128w
128w
128w^2
-128w^2
Clear selection
Q. If z_1 and z_2 are two non-zero complex numbers such that |z_1 + z_2| = |z_1| + |z_2|, then arg (z_1) – arg (z_2) is equal to
2 points
-pi
-pi/2
0
i
Clear selection
Q. The inequality | z – 4| < |z – 2| represents the region given by
2 points
Re (z) >3
Re (z) < 0
Re (z) > 0
None of these
Clear selection
Q. Let z and w be two non-zero complex numbers such that |z| = |w| and arg (z) + arg (w) = pi, then z equals
2 points
-bar (w)
bar (w)
w
-w
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