Question

Let z=x+iy x y in R-{0} and i=sqrt(-1) then (z+bar(z))^(2019)+(z-bar(z))^(2020)+(zbar(z))^(2020) is a.​

Answer 1

Answer:

Here ans is 4

Step-by-step explanation:

Let z=x+iy.

Given, z

2

+

z

=0

or, x

2

−y

2

+2ixy+x−iy=0

or, (x

2

−y

2

+x)+i(2xy−y)=0

Comparing the real and imaginary part we get,

x

2

−y

2

+x=0.......(1) and 2xy−y=0.....(2).

From (2) we get, 2xy−y=0

or, y(2x−1)=0

or, y=0 and x=

2

1

.

When y=0 then from (1) we get, x

2

−x=0 or, x=0,−1.

Again x=

2

1

then from (1) we get, y

2

=

4

1

+

2

1

=

4

3

or, y=±

2

3

.

So the solutions, in the form (x,y) are (0,0),(−1,0),(±

2

3

,

2

1

).

So we have 4 solutions.