The polar form of complex number 1 + i is
√2 (cos π/4 + i sin π/4 )
√2 (cos 2π/4 + i sin 2π/4
√2 (cos π/4 - i sin π/4 )
√3 (sin 2π/4 + i cos 2π/4)
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 P is a multiple of n , then the sum of Pth power of nth roots of unity is
p
n
0
None of these
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 z = 1 + i , then the multiplicative inverse of z2 is (where i = √-1 )
2 i
1 - i
-i/2
i/2
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
1
2
If , then the value of x is
cos θ ± i sin θ
cos 2θ + i sin 2θ
(cos θ + i sin θ )2
cos 4θ - i sin 4θ
If 1, a1 , a2 , a3 . . . an-1 are the nth roots of unity , then the value of (1 - a1) (1 - a2) (1 - a3) . . . (1 - an-1) is
- n
