Two lines z i − z ˉ i + 2 = 0 and z ( 1 + i ) + z ˉ ( 1 − i ) + 2 = 0 intersect at P . The complex numbers of points on the second line which are at a distance of 2 unit form the point P are z = i ± e

Question

Two lines z i − z ˉ i + 2 = 0 and z ( 1 + i ) + z ˉ ( 1 − i ) + 2 = 0 intersect at P . The complex numbers of points on the second line which are at a distance of 2 unit form the point P are z = i ± e i k π ​ , find k

TestHub · Accepted Answer

k = 4 The lines are z i − z ˉ i + 2 = 0 and z ( 1 + i ) + z ˉ ( 1 − i ) + 2 = 0 at i . Let point on the line be z then ∣ z − i ∣ = 2 ⇒ 2 e i θ + i putting this in second equation ⇒ θ = π /4 ∴ points are z = i ± e iπ /4

Mathematics - Complex Number Question with Solution | TestHub

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