Question

In the above question the maximum value of ŠPAB + ŠPBC + ŠPCD + ŠPDA is equal to-

• A. $\frac{3\pi}{4}$
• B. $\frac{\pi}{4}$
• C. $\frac{5\pi}{4}$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (C)

$\frac{5\pi}{4}$

Answer 2

Sol. 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 $\frac{3\pi}{4}$