If we express ( 2 + 3 i ) 2 in the form of ( x + iy ) , we get
-5 + 12 i
12 - 5 i
5 - 12 i
12 + 5 i
If the complex numbers z1,z2 and z3 represent the vertices of an equilateral triangle such that | z1 | = | z2 | = | z3 | , then the sum of z1,z2 and z3 is
-1
0
1
2
The value of is
1/5
-1/5
1/10
-1/10
If |z - 3 + i | = 4, then the locus of z = x + iy is
x2 + y2 = 0
x2 + y2 - 6 = 0
x2 + y2 - 3x + y - 6 = 0
x2 + y2 - 6 x + 2 y - 6 = 0
If we express in the form of x + iy, we get
cos 49θ - i sin 49θ
cos 23θ + i sin 23θ
cos 49θ + i sin 49θ
cos 21θ + i sin 21θ
If the amplitude of a complex number is π/2, then the number is
Purely imaginary
Purely real
Neither real nor imaginary
If -i + 3 is a root of x2 - 6x + k = 0 then the value of k is
5
√5
√10
10
If z1,z2 and z3 be the vertices of an equilateral triangle occurring in anticlockwise sense, then
z1 + z2 + z32 = 0
z1z2 + z2z3 + z3z1 = 0
z1 + ω z2 + ω2 z3 = 0
z12 + z22 + z32 = 2 (z1z2 + z2z3 + z3z1)
The solution of the equation | z | - z = 1 + 2i is
2 - 3/2 i
3/2 + 2i
3/2 - 2i
-2 + 3/2 i
If conjugate and reciprocal of a complex number z = x + iy are equal , then
x + y = 1
x2 + y2 = 1
x = 1 and y = 0
x = 0 and y = 1