Question

Let the vertices of the square ABCD are 1, –1, i and –i in the Argand Diagram. Let P be represented by z, then ŠPAB+ ŠPBC + ŠPCD + ŠPDA = arg $\left( \frac{z^{4} - 1}{4} \right)$= arg (z⁴ –1).

Since z⁴ also lies inside the square Ž$\frac{5\pi}{4}$³ arg (z⁴ –1) ³$\frac{3\pi}{4}$

• A. Circle with radius 1 and centre (0, 1)
• B. Circle with radius 2 and centre (1, 0)
• C. Straight line
• D. Circle with radius 3 and centre at the origin

Answer 1

Answer: (B)

Circle with radius 2 and centre (1, 0)

Answer 2

Sol. Let W = 1 + 2Z. Then W –1 = 2Z

\ |W –1| = 2 |Z| = 2 for points on |Z| = 1

\ the locus of W is a circle with centre at (1, 0) and radius 2 when |Z| = 1.