Algebra of Complex Numbers
Trending Questions
Q.
If c+ic−i = a+ib, where a, b, c are real, then a2+b2 =
1
-1
c2
−c2
Q.
The value of 2+3i4+5i is
8+15i23
2i+2341
3 + 81i
None of these
Q. Let (−2−13i)3=x+iy27 (i=√−1), where x and y are real numbers, then y−x equals:
- 91
- 85
- −91
- −85
Q. Let α, β, γ and a, b, c are the complex numbers such that αa+βb+γc=1+i and aα+bβ+cγ=0. If α2a2+β2b2+γ2c2=p+iq, where p, q∈R, then the value of p+q is
Q. If α, β∈R are such that 1−2i (here i2=−1) is a root of z2+αz+β=0, then (α−β) is equal to
- 7
- −3
- 3
- −7
Q. Express (2+3i)3 in the form (a+ib)
- −46+9i
- −40+7i
- 46−9i
- 46+9i
Q. If A={y:x2+y2<1, x∈N} and B={y:x2+y2=4, x∈N}, then n(A×B) is
- 0
- 1
- 3
- infinite
Q.
1−i1+i is equal to
cosπ2+isinπ2
cosπ2-isinπ2
sinπ2+icosπ2
None of these
Q. If 2a+b+ca, a+2b+cb and a+b+2cc are in A.P., then
- a, b, c are in A.P.
- 1a, 1b, 1c are in A.P.
- a, c, b are in A.P.
- 1a, 1c, 1b are in A.P.
Q.
The value of 12−3i+7+8i is
14−24i5
9+5i13
90+55i13
93+107i13
Q. If −4≤|x|≤2, then x belongs to
- [−4, 2]
- [2, 4]
- [−4, 4]
- [−2, 2]
Q.
The value of 2+3i4+5i is
8+15i23
2i+2341
3 + 81i
None of these
Q. If w=α+iβ, where β≠0 and z≠1, satisfies the condition that (w−¯wz1−z) is purely real, then the set of values of z is
- |z|=1, z≠2
- |z|=1, and z≠1
- z=¯z
- None of these
Q. If z=−5+3i and the value of z4+9z3+26z2−14z+8 is k, where k∈R, then the value of −k is
Q. If z=3+2i, then value of 3z3−13z2+9z+65 is
- 0
- 1
- 2
- 3
Q. If the imaginary part of 2z+1iz+1 is −2, then the locus of z is
- a circle
- a straight line
- an ellipse
- a parabola
Q. If Z2+kZ+1−2i=0 has roots as z1 and z2, where z1=−i and k∈R, then the value of k is
- −2
- 2
- −1
- 1
Q. If z=2+i and z3+3z2−9z+8=a+ib, then the value of a+b is
Q.
If x=-5+√−4, then the value of the expression x4+9x3+35x2-x+4 is
160
-160
60
-60
Q.
1+7i(2−i)2=
√2 [cos3π4+isin3π4]
√2 [cosπ4+isinπ4]
[cos3π4+isin3π4]
None of these
Q.
The equation ¯¯bz+¯¯¯zb where b is a non-zero complex constant and c is real, represents
A circle
A straight line
A parabola
None of these
Q. The real order pair (x, y) which satisfies (x4+2xi)−(3x2+yi)=(3−5i)+(1+2yi) is
- (−2, 13)
- (2, 3)
- (−2, 3)
- (2, 13)
Q. Match List I with List II and select the correct answer using the code given below the lists :
List IList II (A)Let z, ω, α be complex numbers such that(P)0|z|=|ω|=4 and α=z−¯¯¯ω16+z ¯¯¯ω. Then Re (α) is equal to (B)If x=p+iq is a complex number such that(Q)3x2=3+4i and x3=2+11i, where i=√−1, then p+q is equal to(C)Number of complex number(s) z satisfying the(R)4equation ¯¯¯z=iz2, where i=√−1, is equal to(D)If z∈C satisfies |z+2−i|=5, then the(S)5maximum value of |3z+9−7i|4 is equal to
Which of the following is the only CORRECT combination?
List IList II (A)Let z, ω, α be complex numbers such that(P)0|z|=|ω|=4 and α=z−¯¯¯ω16+z ¯¯¯ω. Then Re (α) is equal to (B)If x=p+iq is a complex number such that(Q)3x2=3+4i and x3=2+11i, where i=√−1, then p+q is equal to(C)Number of complex number(s) z satisfying the(R)4equation ¯¯¯z=iz2, where i=√−1, is equal to(D)If z∈C satisfies |z+2−i|=5, then the(S)5maximum value of |3z+9−7i|4 is equal to
Which of the following is the only CORRECT combination?
- (C)→(S), (D)→(P)
- (C)→(P), (D)→(Q)
- (C)→(Q), (D)→(R)
- (C)→(R), (D)→(S)
Q.
1−i1+i is equal to
cosπ2+isinπ2
cosπ2-isinπ2
sinπ2+icosπ2
None of these
Q. The real values of x and y for which (x−13+i+y−13−i)=i is
- x=−4 and y=6
- x=−6 and y=3
- x=2 and y=8
- x=8 and y=−6
Q.
The least positive integer n which will reduce (i−1i+1)nto a real number , is
2
3
4
5