A to Z Exams

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

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

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

ABC is an isosceles triangle and B= 900. If B and the midpoint P of AC are represented by 3+2i and 1-i then the other vertices are

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

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

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

(3+5ω+3ω2)6=

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

(1/1+2ω)-(1/1+ω)+(1/2+ω)=

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

(a+2b)2+(aω+2bω2)2+(aω2+2bω)2=

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

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

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

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

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

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

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

The amplitude of 1+cos θ+ i sin θ is

(1+ω-ω2) (1-ω+ω2)=

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

(2+ω2+ω4)5

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

If α and β are complex cube roots of unity, then α4+β4+α-1β-1=

i2+i-4+i-6+…(2n+1) terms

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

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

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

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