Question

The sum of amplitude of z and another complex number is $z = 1 - \cos\alpha + i\sin\alpha$. The other complex number can be written.

• A. $z$
• B. $\frac{\alpha}{2}$
• C. z
• D. $- \frac{\alpha}{2}$

Answer 1

Answer: (B)

$\frac{\alpha}{2}$

Answer 2

We have $= x - iy$ and let their complex $a,b,x,y \in R.$ and given that

$\mathbf{\therefore}$

$\mathbf{|1 - i}\mathbf{|}^{\mathbf{x}}\mathbf{=}\mathbf{2}^{\mathbf{x}}$; $\mathbf{(}\sqrt{\mathbf{2}}\mathbf{)}^{\mathbf{x}}\mathbf{=}\mathbf{2}^{\mathbf{x}}$

$\mathbf{2}^{\mathbf{x/2}}\mathbf{=}\mathbf{2}^{\mathbf{x}}$

which lies in second quadrant, i.e. $\frac{x}{2} = x$.