What is the locus of z, if amplitude of z – 2 – 3i is π/4 ?

Question 1

Question 2

Let z = x + iy. Then z – 2 – 3i = (x – 2) + i (y – 3)

Let θ be the amplitude of z – 2 – 3i. Then tanθ = (y-3)/(x-2)

⇒ tan π/4 = (y-3)/(x-2) [since θ=π/4 ]

⇒ 1 = (y-3)/(x-2) i.e. x – y + 1 = 0

Hence, the locus of z is a straight line.

kratos · Answer 1 · 2020-11-24T16:57:38+0000

Let z = x + iy. Then z – 2 – 3i = (x – 2) + i (y – 3)

Let θ be the amplitude of z – 2 – 3i. Then tanθ = (y-3)/(x-2)

⇒ tan π/4 = (y-3)/(x-2) [since θ=π/4 ]

⇒ 1 = (y-3)/(x-2) i.e. x – y + 1 = 0

Hence, the locus of z is a straight line.

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