A to Z Exams

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

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

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

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

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

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

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

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

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

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

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

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

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

(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 =

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

(a+bω+cω2)/(c+aω+bω2)=

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

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

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

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 sin2θ)= x+iy, then y=

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

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

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

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

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

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

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