Find the area of the region bounded by arg|z|≤π/4 and |z-1|<|z-3|.
Find the area of the region bounded by arg|z|≤π/4 and |z-1|<|z-3|. Correct Answer 4 sq. units
|z-1|<|z-3| ⇒ (x-1)2+y2<(x-3)2+y2 ⇒ x<2. Therefore, a triangle is formed with base length 4 and height 2 (along x-axis). Hence, the required area=1/2×4×2=4.
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Feb 20, 2025
