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Question
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
Solution
Let z = x + iy.
Then z – 2 – 3i = (x – 2) + i(y – 3)
Let θ be the amplitude of z – 2 – 3i.
Then `tan theta = (y - 3)/(x - 2)`
⇒ `tan pi/4 = (y - 3)/(x - 2)("since" theta = pi/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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