Finding length of a complex number

[Niles]

Homework Statement

Hi all.

Please take a look at this complex number:

<br /> \widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B,<br />

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:

<br /> |\widehat C| = \frac{|1-\widehat a|}{|1+\widehat a|}|\widehat B|<br />

Thanks in advance.Niles.

 

[Hootenanny]

Homework Statement

Hi all.

Please take a look at this complex number:

<br /> \widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B,<br />

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:

<br /> |\widehat C| = \frac{|1-\widehat a|}{|1+\widehat a|}|\widehat B|<br />

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.