The amplitude of the complex number 1 + sinα - i cos α is

Question

The amplitude of the complex number 1 + sinα - i cos α is (A)  (π/4)  (B)  α - (π/4)  (C)  (π/2) - (π/4)  (D)  (π/4)-α

Tardigrade Admin · Accepted Answer

Let z=1+ sin α-i cos α operatornameamp(z) = tan -1((- cos α/1+ sin α)) =- tan -1(( cos α/1+ sin α)) =- tan -1(( cos 2 (α/2)- sin 2 (α/2)/( cos (α)2+ sin (α)2)) =- tan /-1)(( cos (α/2)- sin (α/2)/ cos (α)2+ sin (α)2) =- tan /-1)( tan (π/4)-(α/2)) =-((π/4)-(α/2))=(α/2)-(π/4)

Q. The amplitude of the complex number $1 + sin α - i cos α$ is

$\frac{π}{4}$

$α - \frac{π}{4}$

$\frac{π}{2} - \frac{π}{4}$

$\frac{π}{4} - α$

Q. The amplitude of the complex number 1+sinα−icosα is

4π​

α−4π​

2π​−4π​

4π​−α

Let z=1+sinα−icosα amp(z)=tan−1(1+sinα−cosα​) =−tan−1(1+sinαcosα​) =−tan−1((cos2α​+sin2α​)cos22α​−sin22α​​) =−tan−1(cos2α​+sin2α​cos2α​−sin2α​​) =−tan−1(tan4π​−2α​) =−(4π​−2α​)=2α​−4π​

Q. The amplitude of the complex number $1 + sin α - i cos α$ is

$\frac{π}{4}$

$α - \frac{π}{4}$

$\frac{π}{2} - \frac{π}{4}$

$\frac{π}{4} - α$