Question

if z = 1-cos theta + i sin theta , |z|= ​

Answer 1

Answer:

The answer is $2\sin\frac{\theta}{2}$

Step-by-step explanation:

• Concept: If $z=a+ib$, then $|z|=\sqrt{a^2+b^2}$

 

           Given  $z=(1-\cos\theta)+i\sin\theta$

             $\Rightarrow |z|=\sqrt{(1-\cos\theta)^2+\sin^2\theta}$

                    $=\sqrt{1-2\cos\theta+\cos^2\theta+\sin^2\theta}\\=\sqrt{1-2\cos\theta+1}=\sqrt{2(1-\cos\theta)}\\\\=\sqrt{2(2\sin^2\frac{\theta}{2})}=2|\sin\frac{\theta}{2}|$