Question

If z₁= $\left[2(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}})\right]$ is rotated about origin by 60° in anti-clockwise direction, which of the following is/are correct (assume z is the final vector)

• A. arg(z) =
• B. arg(z) =
• C. = 1
• D. = 2

Answer 1

Answer: (A), (D)

The correct options are
A arg(z) =
D = 2

We will find the modulus and argument of z1 first. this will help us in rotating it and finding the final vector z.

$z_1$ = $\left[2(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}})\right]$

arg ($z_1$ ) = $ta{n}^{-1}$ $\left(\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}\right)$

= $ta{n}^{-1}$ (1)

= $\frac{\pi }{4}$

$\left|z\right|$ = 2

$z_1$ is rotated through angle of 60 $\frac{\pi }{3}$ to reach z.

Clearly, $\left|z\right|$ = $\left|z_1\right|$

= 2

and arg (z) = $\frac{\pi }{4}$ + $\frac{\pi }{3}$

= $\frac{7\pi }{12}$