Question

Find the locus of z given by ।z-1।=।2z-3।.

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

Answer:

3y² = 3x² -10x +8

Step-by-step explanation:

z=x+iy

∣z−1∣=∣2z−3∣                                  …… (1)

Substitute the value of z in equation (1).

⇒ ∣(x +iy)−1∣=∣2(x +iy)−3∣

Simplify the above equation

⇒ ∣x+iy-1∣ = ∣2x+2iy-3∣

⇒ ∣(x-1)+iy∣ = ∣(2x-3)+2iy∣

⇒ $\sqrt{(x-1)^{2}+(iy)^{2} } =\sqrt{(2x-3)^{2}+(2iy)^{2} }$

⇒x² -2x +1 - y² = 4x² - 12x +9 - 4y²          (as i² = -1)

⇒3y² = 3x² -10x +8

IF the answer is correct then brainlest it .