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CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 8 - MCQExams.com

If a+ib=101k=1ik, then (a,b) equals 
  • (0,1)
  • (1,0)
  • (0,1)
  • (1,1)
If z=3i, find |z|.
  • 10
  • 9
  • 8
  • 7
The real part of (1cosθ+2isinθ)1 is:
  • 2sinθ(1cosθ)2+4sin2θ
  • 1+cosθ(1cosθ)2+4sin2θ
  • (1cosθ)2isinθ(1cosθ)2+4i2sin2θ
  • 1cosθ(1cosθ)2+4sin2θ
Which of the following pair of numbers are relatively prime :-
  • 36 and 54
  • 52 and 78
  • 54 and 114
  • 59 and 61
(1+i)32+i  is equal to
  • 2565i
  • 0
  • 15+65i
  • 25+65i
Whether the statement is given true or false
Statement : The product of fifth roots of unity is 1.
  • True
  • False
The modulus of the complex number z=1i34i is
  • 52
  • 25
  • 25
  • none of these
Let z be a complex number such that zc R and 1+z+z21z+z2R, then  |z|=3.
  • True
  • False
If z=1+i2, then the value of z1929 is
  • 1+i
  • 1
  • 1+i2
  • 1+i2
If |Z|=2,|z2|=3,|z3=4| and |z1+z2+z3|=5 then |4z2z3+9z3z1+16z1z2|=
  • 20
  • 24
  • 48
  • 120
If x33+i+y33i=i where x,yR then
  • x=2 & y=8
  • x=2 & y=8
  • x=2 & y=6
  • x=2 & y=8
The locus of z such that |z+iz1|=2
  • straight line
  • circle with radius 2
  • circle with radius 223
  • none of these
nN, (1+i2)8n+(1i2)8n=
  • 0
  • 1
  • 2
  • 2
(1+i1i)4+(1i1+i)4= 
  • 0
  • 1
  • 2
  • 4
The complex number z satisfies z+|z|=2+8i. The value of |z| is
  • 10
  • 13
  • 17
  • 23
If |z1+z2|=|z1|+|z2| where z1 and z2 are different non - zero complex number, then ?
  • Re(z1z2)=0
  • Im(z1z2)=0
  • z1+z2=0
  • None
It z be a complex number and |z+3|8 then the value of |z2| lies in 
  • [2,13]
  • [0,13]
  • [2,13]
  • [13,2]
The number of prime numbers between 1 and 10 is
  • 12
  • 4
  • 3
  • 2
if z1=3+4i and Im(z1z2)=0 Find z2 
  • z2=34i
  • z2=3+4i
  • z2=3±4i
  • None of these
Modulus of cosθisinθsinθicosθ is
  • 0
  • 2θ
  • π2θ
  • None of these

The value of 13n=1(in+in+1), where i=1 equals:

  • i
  • i1
  • i
  • 0
(1+cosπ8+isinπ81+cosπ8isinπ8)8= ?
  • 1+i
  • 1i
  • 1
  • 1
3+2 i sinθ will be real, if θ=
  • 2nπ
  • nπ+π/2
  • nπ
  • none of these
Let zr(1r4) be complex numbers such that |zr|=r+1and|30 z1+20 z2+15z3+12 z4|=k|z1z2z3+z2z3z4+z3z4z1+z4z1z2|. Then value of k equals ?
  • |z1z2z3|
  • |z2z3z4|
  • |z3z4z1|
  • |z4z1z2|

For a complex number z, the minimum value of |z|+|z1| is

  • 1
  • 2
  • 3
  • none of these
If |z1|==1,|z2|=2,, then the value of |z1+z2|2+|z1z2|2 is equal to 
  • 2
  • 3
  • 4
  • none of these
If z1, z2 are two complex numbers such that arg(z1+z2)=0 and Im(z1z2)=0, then
  • z1=z2
  • z1=z2
  • z1=¯z2
  • none of these
23=
  • -6
  • 6
  • i6
  • i6
The argument of the complex number sin6π5+i(1+cos6π5) is
  • 6π5
  • 5π6
  • 9π10
  • 2π5
If |z|=1, then |z1| is
  • < |arg(z)|
  • > |arg(z)|
  • = |arg(z)|
  • None of these
If z is a complex number such that |z|2, then the minimumm value of |z+12|:
  • is equal to 52
  • lies in the interval (1,2)
  • is strictly greater then 52
  • is strictly greater than 32 but less than 52
If |z|=1 and |ω1|=1 where z,ωC, then the largest set of values of |2z1|2+|2ω1|2 equals  
  • [1,9]
  • [2,6]
  • [2,12]
  • [2,18]
If Z is a complex number such that |z|2,
then the minimum value of |z+12|
  • Is equal to 52
  • Lies in the interval (1,2)
  • Is strictly grater than 52
  • Is strictly greater than 32 but less than 52
if z1=3+7i then |z1| is 
  • 28
  • 58
  • 68
  • none of these
If z1 and z2 two complex numbers satisfying the equation |z1+iz2z1iz2|=1 then z1z2 is a
  • purely real
  • of unit modulus
  • purely imaginary
  • none of these
Mark the correct alternative of the following.
Which of the following is a prime number?
  • 263
  • 361
  • 323
  • 324
let |z+ˉz|+|zˉz|=2014. Then z lies on a
  • Circle
  • Straight line
  • Square
  • Rectangle
Argument and modules of [1+i1i]2πi are respectively................. 
  • π2 and 1
  • π2 and 2
  • 0 and 2
  • π2 and 1
Choose the composite numbers from the following numbers 87,67,45,34,23,27,33.
  • 45,87,34,27,33
  • 45,87,67,33
  • 33,27,23,34
  • All the above
  • None of these
If |z1z2|=1 and arg(z1z2)=0 , then
  • z1=z2
  • |z2|2=z1z2
  • z1z2=1
  • z1=z2
If x2+y2=1 and x1 then 1+y+ix1+yix
  • 1
  • y+ix
  • 2
  • x+ix
Im (a+ia4+a2+1)=
  • 12a2a+1
  • a2a+a2
  • 12a2+a+1
  • a2a+12
If for complex number z1andz2arg(z1)arg(z2)=0thenz1z2 is equal to:
  • z1+z2
  • z1+z2
  • z1z2
  • 0
If z=(3+7i)(p+iq) where p,qI{0}, is purely imaginary then minimum value of |z|2 is
  • 0
  • 58
  • 33643
  • 3364
If z(1) is complex number such that z1z+1 is purely imaginary, then |z| is equal to
  • 1
  • 2
  • 3
  • 5
z=a+ib, a,b,R, b0 and |z|=1, then z=c+ici, where c is equal to
  • ab
  • a1b
  • a+1b
  • a+1b+1
If z is a complex number, then z2+ˉz2=2 represents-
  • a circle
  • a straight line
  • a hyperbola
  • an ellipse
The modulus of the complex number z=(1i3)(cosθ+isinθ)2(1i)(cosθisinθ)  is-
  • 122
  • 13
  • 12
  • 123
If |z+2i|=5 then the maximum value of |3z+97i| is 
  • 18
  • 19
  • 20
  • 8
If |z|=1 and ϖ=z1z+1, where z1, then Re(ϖ) is
  • 0
  • 1|z+1|2
  • 12|z+1|2
  • 2|z+1|2
0:0:1


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