Eamcet - Maths - Complex Numbers Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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Express 4+3i/(2+3i)(4-3i) in the form of x+iy

  

  

  

  

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

  

  

  

  

i2+i-4+i-6+…(2n+1) terms

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

  

  

  

  

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

  

  

  

  

If the roots of (z - 1)n = i(z + 1)n are plotted in the argand diagram they are:

  

  

  

  

The modules of (3+2i)(2-i)/ (1+i) is

  

  

  

  

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

  

  

  

  

The complex numbers sin x+ i cos 2x- i sin 2x are conjugate to each other for

  

  

  

  

The conjugate of (1+2i) (2-3i) is

  

  

  

  

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

  

  

  

  

If three complex numbers are in A.P. then they lie on

  

  

  

  

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

  

  

  

  

If a and b are numbers between 0 and 1 such that the points z1= a+i, z2= 1+bi and z3= 0 from an equilateral triangle then a,b are

  

  

  

  

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

  

  

  

  

If x= -5+4i then x4+9x3+35x2-x+4=

  

  

  

  

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

  

  

  

  

If 3/(2+ cos θ+ i sin θ)= x+iy then (x-1)(x-3)=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If x=-5+4i then x4+9x3+35x2-x+4=

  

  

  

  

(a+2b)2+(aω+2bω2)2+(aω2+2bω)2=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The modulus of (3-4i)(4+5i) is

  

  

  

  

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