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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(1-ω+ω2)(1-ω2+ω4) (1-ω4+ω8) (1-ω8+ω16)=

  

  

  

  

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

  

  

  

  

Express 4+3i/(2+3i)(4-3i) in the form of x+iy

  

  

  

  

(3+5ω+3ω2)6=

  

  

  

  

If ω is a complex cube root of unity, then sin[(ω10+ω23)π-π/4]=

  

  

  

  

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

  

  

  

  

The modules of √3+i/(1+i)(1+√3i) is

  

  

  

  

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

  

  

  

  

The amplitude of 1+cos θ+ i sin θ is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Express (3-2i/ 5+4i)+ (3+2i/ 5-4i) in the form of a+ib

  

  

  

  

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

  

  

  

  

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

  

  

  

  

(a+2b)2+(aω+2bω2)2+(aω2+2bω)2=

  

  

  

  

If z= (λ+3)+i√(5-λ2), then the locus of z is a circle with centre at

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The equation of the line joining the points represented by 2-3i and -3+4i in the Argand plane is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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