Complex numbers

[cyrexia]

let be z,u [imath]\isin \Complex[/imath] ,
z*u [imath]\ne[/imath] -1 with |z| = |u| = 1

demonstrate that [imath]\dfrac{z+u}{1+zu}[/imath] [imath]\isin[/imath] [imath]\R[/imath]

 

[Dr.Peterson]

let be z,u [imath]\isin[/imath] [imath]\Complex[/imath] , z*u [imath]\ne[/imath] -1 with |z|=|u|=1
demonstrate that [imath]\frac{z+u}{1+zu}[/imath] [imath]\isin[/imath] [imath]\R[/imath]

Please show us where you are stuck.

Did you multiply the numerator and the denominator by the conjugate of the denominator, as usual?

 

[blamocur]

Is there a typo there? Consider [imath]z = u = i[/imath]. Then [imath]z^\star u = 1 \neq -1[/imath], but [imath]\frac{z+u}{1+zu} = \frac{2i}{1-1} = \infty[/imath]