Eamcet - Maths - Complex Numbers

Express (a+ib/ a-ib)+(a-ib/ a+ib) in the form of a+ib

A.  (a2+b2)/( a2 -b2)

B.  (a2-b2)/( a2 +b2)

C.  2 (a2+b2)/( a2 -b2)

D.  2(a2-b2)/( a2 +b2)

View Answer  

Correct Answer :

2(a2-b2)/( a2 +b2)



Explanation :
No Explanation available for this question

If (a+ib)2= x+iy then x2+y2=

A.  0

B.  1

C.  (a2+b2)2

D.  (a2-b2)2

View Answer  

Correct Answer :

(a2+b2)2



Explanation :
No Explanation available for this question

For all values of a and b(a + 2b)x + (a- b)y + (a + 5b) = 0 passes through the point:

A.  (-1, 2)

B.  (2, -1)

C.  (-2, 1)

D.  (1, -2)

View Answer  

Correct Answer :

(-2, 1)



Explanation :
No Explanation available for this question

If the direction ratio of two lines are given by 3lm-4ln+mn =0 and l+2m+3n=0,then the angle between the lines, is

A.  π/6

B.  π/4

C.  π/3

D.  π/2

View Answer  

Correct Answer :

π/2



Explanation :
No Explanation available for this question

The ascending order of the moduli of the complex numbers z1=1+i,z2=1+2i,z3=1-i/√2,z4=3+4i is

A.  z1,z2,z3,z4

B.  z4,z2,z1,z3

C.  z3,z1,z2,z4

D.  z4,z3,z2,z1

View Answer  

Correct Answer :

z3,z1,z2,z4



Explanation :
No Explanation available for this question

The period of the function tan(3x+5) is:

A.  2π/3

B.  π/6

C.  π/3

D.  π

View Answer  

Correct Answer :

π/3



Explanation :
No Explanation available for this question

I: The modulus of √3+i/(1+i)(1+√3i) is 1/√2 II: The least positive value of n for which (1-i/1+i)n=1 is 2

A.  only I is true

B.  only II is true

C.  both I and II are true

D.  neither I nor II are true

View Answer  

Correct Answer :

both I and II are true



Explanation :
No Explanation available for this question

If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:

A.  1

B.  ω

C.  ω2

D.  ω3

View Answer  

Correct Answer :

ω2



Explanation :
No Explanation available for this question

If (cos 3α+i sin 3α)(cos 5β+i sin 5β)= cos θ+i sin θ then θ is

A.  2α+3β

B.  3α+6β

C.  3α+5β

D.  2α+4β

View Answer  

Correct Answer :

3α+5β



Explanation :
No Explanation available for this question

If x+iy= cis α cis β then the value of x2+y2 is

A.  0

B.  1

C.  -1

D.  2

View Answer  

Correct Answer :

1



Explanation :
No Explanation available for this question

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

A.  x3+y3+z3+3xyz

B.  x3+y3+z3-3xyz

C.  x3+y3+z3

D.  none

View Answer  

Correct Answer :

x3+y3+z3-3xyz



Explanation :
No Explanation available for this question

If  |z-1/z+a|=1 where Re(a)≠0 then the locus of z=x+iy is

A.  y=0

B.  x=0

C.  x2+y2+2x-4y=0 such that y1

D.  x2+y2+2x-4y=0 such that 2x-y+4>0

View Answer  

Correct Answer :

x=0



Explanation :
No Explanation available for this question

The region represented by |z+a|+|z-a|

A.  x2+y2

B.  x2+y2>4a2

C.  x2-y2

D.  none

View Answer  

Correct Answer :

none



Explanation :
No Explanation available for this question

If a=2i+2j+k, a.b=14, axb=3i-j-8k then b=

A.  5i+j+2k

B.  5i-5j+2k

C.  5i+5j-2k

D.  5i-5j-2k

View Answer  

Correct Answer :

5i+j+2k



Explanation :
No Explanation available for this question

(1/1+2ω)-(1/1+ω)+(1/2+ω)=

A.  ω

B.  ω2

C.  a2+b2

D.  0

View Answer  

Correct Answer :

0



Explanation :
No Explanation available for this question

If ω is a complex cube root of unity then ( 1 - ω + ω2)6 + ( 1- ω2 + ω)6 =

A.  0

B.  6

C.  64

D.  128

View Answer  

Correct Answer :

128



Explanation :
No Explanation available for this question

(1+ω)(1+ω2) )(1+ω3)(1+ω4)(1+ω5) (1+ω6)...(1+ω3n)=

A.  23n

B.  22n

C.  2n

D.  none

View Answer  

Correct Answer :

2n



Explanation :
No Explanation available for this question

(a+bω+cω2)/(c+aω+bω2)=

A.  ω

B.  ω2

C.  a2+b2

D.  0

View Answer  

Correct Answer :

ω2



Explanation :
No Explanation available for this question

If (1 + cos θ + i sin θ)(1 + cos 2θ + i sin 2θ)=x+iy then y=

A.  16 cos2θ sin2(θ/2)

B.  16 sin2θ cos2(θ/2)

C.  16 sin2θ sin2(θ/2)

D.  16 cos2θ cos2(θ/2)

View Answer  

Correct Answer :

16 cos2θ cos2(θ/2)



Explanation :
No Explanation available for this question

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

A.  (l2-m2)/(l2+m2)

B.  (l2+m2)/(l2-m2)

C.  2lm/(l2+m2)

D.  2lm/(l2-m2)

View Answer  

Correct Answer :

(l2-m2)/(l2+m2)



Explanation :
No Explanation available for this question

If x+iy= 1/1+ cos θ+ i sin θ, then 4x2=

A.  0

B.  1

C.  2

D.  3

View Answer  

Correct Answer :

1



Explanation :
No Explanation available for this question

If x2+x+1=0, then the value of (x+1/x)2+(x2+1/x2)2+...+(x27+1/x27)2 is

A.  27

B.  72

C.  45

D.  54

View Answer  

Correct Answer :

54



Explanation :
No Explanation available for this question

If (1+ cos θ+ i sin θ)(1+ cos 2θ+i sin2θ)= x+iy, then y=

A.  x tan(3θ/2)

B.  x tan(5θ/2)

C.  x tan(7θ/2)

D.  x tan(9θ/2)

View Answer  

Correct Answer :

x tan(3θ/2)



Explanation :
No Explanation available for this question

If u+iv= 2+i/z+3, where z=x+iy, then the values of u, v are

A.  2(x+3)+y/(x+3)2+ y2, x-2y+3/ (x+3)2+y2

B.  2(x+2)+y/(x+2)2+ y2, x-2y+3/ (x+2)2+y2

C.  2(x+4)+y/(x+4)2+ y2, x-2y+3/ (x+4)2+y2

D.  none

View Answer  

Correct Answer :

2(x+3)+y/(x+3)2+ y2, x-2y+3/ (x+3)2+y2



Explanation :
No Explanation available for this question

In the Argand plane, the points represented by the complex number s 2-6i, 4-7i, 3-5i and 1-4i form

A.  parallelogram

B.  rectangle

C.  rhombus

D.  square

View Answer  

Correct Answer :

rhombus



Explanation :
No Explanation available for this question

If  ((1+i)x-2i)/(3+i)+((2-3i)y+i/3-i)=I, then (x,y)=

A.  (0,0)

B.  (3,1)

C.  (3,-1)

D.  (-3,1)

View Answer  

Correct Answer :

(3,-1)



Explanation :
No Explanation available for this question

(1-ω+ω2) (1-ω2+ω4) (1-ω4+ω8)... to 2n factors=

A.  2

B.  22n

C.  2n

D.  none

View Answer  

Correct Answer :

22n



Explanation :
No Explanation available for this question

If (a1+ib1)( (a2+ib2)…. (an+ibn)= A+iB, then (a12 +b12)( a22 +b22 )….(an2 +bn2)=

A.  A2+B2

B.  A2-B2

C.  A3+B3

D.  A3-B3

View Answer  

Correct Answer :

A2+B2



Explanation :
No Explanation available for this question

If z1=1+2i,z2=2+3i,z3=3+4i,then z1,z2 and z3 represents the vertices of

A.  Equilateral triangle

B.  Right angled triangle

C.  Equilateral triangle

D.  None

View Answer  

Correct Answer :

Equilateral triangle



Explanation :
No Explanation available for this question

Express (2+3i/ 2-3i)-(2-3i/ 2+3i) in the form of a+ib

A.  24i/13

B.  27i/13

C.  28i/13

D.  30i/13

View Answer  

Correct Answer :

24i/13



Explanation :
No Explanation available for this question