1 3 7 11 Solution1 consider the complex number z 1 i The ca

1, 3 ,7 ,11

Solution

1) consider the complex number z= 1 + i

   The cartesian form of a complex number z = x + iy

real part is x = 1

imaginary part is y = 1

absolute value of z is ((x)² + (y)²) = 2

the angle = tan^-1(y/x) = tan^-1 (1) = /4

The complex conjugate of z = 1 + i is z^* = 1 - i

3)

consider the complex number z= 3 + i3

The cartesian form of a complex number z = x + iy

real part is x = 3

imaginary part is y = - 3

absolute value of z is ((3)² + (-3)²) = 12 = 23

the angle = tan^-1(-3/3) = tan^-1 (-1/3) = - tan^-1 (-1/3) = 5/6

The complex conjugate of z = 3 + i3 is z^* = 3 - i3

7)

consider the complex number z= - 1

The cartesian form of a complex number z = x + iy

real part is x = -1

imaginary part is y =0

absolute value of z is ((-1)² + (0)²) = 1 = 1

the angle = tan^-1(0/(-1)) = tan^-1 (0) = 0

The complex conjugate of z = - 1 is z^* = -1

11)

consider the complex number z= 2(3/2 + i/2 ) = 3 + i

The cartesian form of a complex number z = x + iy

real part is x = 3

imaginary part is y = 1

absolute value of z is ((3)² + (1)²) = (3 + 1) = 4 = 2

the angle = tan^-1(3/1) = tan^-1 (3) = /3

The complex conjugate of z = - 1 is z^* = 3 - i