Question

if (1+i)²/2-i then find the value of x+y​

Answer 1

Step-by-step explanation:

Given Point A=(1+i); A’ = (1+i)^2; B=(2 , -i); and R’= (1+i) ² /(2-i);

I converted all (x,y) coordinates into polar coordinates in the form of Re^(iθ).

Note: At end of computation I revert back to (x,y) coordinates.

1+i = √2 * e^(iπ/4); =>

(1+i)^2 = 2e^(iπ/2);

2-i = √5 *e^(-iθ); with θ = arctan (1/2); =>

(1+i) ² /(2-i) = 2e^(iπ/2) / √5 *e^(-iθ) =√4 * e^(iπ/2) / √5 *e^(-iθ) ; =>

(1+i) ² /(2-i) = √4/5 * e^(i(π/2 +θ) = √4/5( cos(π/2 +θ) + i sin (π/2 +θ))= >

(1+i) ² /(2-i) = -2/5 + i4/5