Question

Argument and modulus of $x^{2} + \sqrt{(y - 5)^{2}}$ are respectively.

• A. $\sqrt{(x - y)^{2} + 5^{2}}$and 1
• B. $\sqrt{x^{2} + (y - 5)^{2}}$and $\left| (1 + i)\frac{(2 + i)}{(3 + i)} \right| =$
• C. 0 and $- \frac{1}{2}$
• D. $\frac{1}{2}$and 1

Answer 1

Answer: (D)

$\frac{1}{2}$and 1

Answer 2

$\pi$

Now $z = 0 + ib$

⇒ $b > 0$

$arg(z) = \frac{\pi}{2}z = 0 + ib$

$b < 0z$

By De Moivre's Theorem,

$y -$

Hence the amplitude is $arg(z) = - \frac{\pi}{2}$ and modulus is 1.

Trick : $a < 0$

$z$

$arg(z) = \pi$.