### Eamcet - Maths - Complex Numbers Test

#### Time Left : 00 : 30    : 00

(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

Note: