Finding length of a complex number

[Niles]

Homework Statement

Hi all.

Please take a look at this complex number:

$$\widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B,$$

where a hat indicates that the number is complex. Can you confirm me in that the length (modulus) of this complex number $|\widehat C|$ is given by:

$$|\widehat C| = \frac{|1-\widehat a|}{|1+\widehat a|}|\widehat B|$$

Thanks in advance.Niles.

 

[Hootenanny]

Homework Statement

Hi all.

Please take a look at this complex number:

$$\widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B,$$

where a hat indicates that the number is complex. Can you confirm me in that the length (modulus) of this complex number $|\widehat C|$ is given by:

$$|\widehat C| = \frac{|1-\widehat a|}{|1+\widehat a|}|\widehat B|$$

Thanks in advance.Niles.

Yes, but you need to be careful. Note that if $\widehat{a} = \alpha + i\beta$ then

$$\left|1-\widehat{a}\right| = \sqrt{\left(1-\alpha\right)^2 + \beta^2}$$

 

[Niles]

Thanks a lot for responding quickly.