Q14 of 66 Page 91

Show that represents a circle. Find its centre and radius.

Given

Substituting z = x + iy, we get

⇒ |x – 2 + iy| = 2 |x – 3 + iy|

⇒ x² – 4x + 4 + y² = 4 (x² – 6x + 9 + y²)

⇒ 3x² + 3y² – 20x + 32 = 0

Hence, centre of circle is (10/3, 0) and radius is 2/3.

If |z + 1| = z + 2 (1 + i), then find z.

If arg (z – 1) = arg (z + 3i), then find x – 1 : y. where z = x + iy

If is a purely imaginary number (z ≠ –1), then find the value of |z|.

z₁ and z₂ are two complex numbers such that |z₁| = |z₂| and arg (z₁) + arg (z₂) = π, then show that