Can anyone help me solve this?

((1+i)/(1−i))^2 + 1/(x+yi) = 5+3i

1/(x+yi) = 5+3i - ((1+i)/(1−i))²

1/(x+yi) = ( (5+3i)(1−i)² - (1+i)² )/(1−i)²

1/(x+yi) = ( (6-10i) - (0+2i) )/(0-2i)

1/(x+yi) = (6-12i)/(0-2i)

1/(x+yi) = 6+3i

1+0i = (6+3i)(x+yi) = (6x-3y) + (3x+6y)i

3x+6y = 0 and 6x-3y = 1

The simultaneous solution to these equations is x = 2/15 and y = -1/15.

Simplify ((1 + i) / (1 - i))^2 first

((1 + i) / (1 - i))^2 =>

((1 + i) * (1 + i) / ((1 - i) * (1 + i)))^2 =>

((1 + 2i + i^2) / (1^2 - i^2))^2 =>

((1 + 2i - 1) / (1 - (-1)))^2 =>

(2i / 2)^2 =>

i^2 =>

-1

-1 + 1 / (x + yi) = 5 + 3i

(-1 * (x + yi) + 1) / (x + yi) = 5 + 3i

(1 - x - yi) / (x + yi) = 5 + 3i

((1 - x) - yi) * (x - yi) / (x^2 - y^2 * i^2) = (5 + 3i)

((1 - x) * x - (1 - x) * yi - xy * i + y^2 * i^2) / (x^2 + y^2) = 5 + 3i

(x - x^2 - y^2 + (x - 1) * y * i - xy * i) / (x^2 + y^2) = 5 + 3i

(x - x^2 - y^2 + xyi - yi - xyi) / (x^2 + y^2) = 5 + 3i

(x - x^2 - y^2 - yi) / (x^2 + y^2) = 5 + 3i

x / (x^2 + y^2) - (x^2 + y^2) / (x^2 + y^2) - (y/(x^2 + y^2)) * i = 5 + 3i

x / (x^2 + y^2) - 1 - (y/(x^2 + y^2)) * i = 5 + 3i

x / (x^2 + y^2) - (y/(x^2 + y^2)) * i = 6 + 3i

x / (x^2 + y^2) = 6

-y / (x^2 + y^2) = 3

x / 6 = x^2 + y^2

-y / 3 = x^2 + y^2

x/6 = -y/3

x = -2y

x / (x^2 + y^2) = 6

-2y / ((-2y)^2 + y^2) = 6

-2y / (4y^2 + y^2) = 6

-2y / (5y^2) = 6

-2 / (5y) = 6

-2 = 30y

-1 = 15y

-1/15 = y

x = -2y

x = 2/15