The figure in the complex plane given by 10 z z ¯ - 3 z 2 + z ¯ 2 + 4 i z 2 - z ¯ 2 = 0

Step-by-step solution

10 z z ¯ - 3 ( z + z ¯ ) 2 - 2 z z ¯ + 4 i ( ( z + z ¯ ) ( z - z ¯ ) ) = 0 Let   z = x + i y 10 x 2 + y 2 - 3 4 x 2 - 2 x 2 - 2 y 2 + 4 i ( 2 x ( 2 i y ) ) = 0 ⇒ 4 x 2 + 16 y 2 - 16 x y = 0 ⇒ x 2 - 4 x y + 4 y 2 = 0 ⇒ ( x - 2 y ) 2 = 0 ⇒ x = 2 y ∴ straight line