complex no question (1 Viewer)

[skepticality]

hey, im a bit newb.
help would be a appreciated

Simplify the expression, in the pic

 

[icycloud]

Let z = 5 + 12i, conj(z) = Z = 5-12i

Expression becomes:

[Sqrt(z) + Sqrt(Z)] / [Sqrt(z) - Sqrt(Z)]
= [Sqrt(z) + Sqrt(Z)]^2 / [z - Z]
= (z + Z + 2Sqrt(zZ)) / (z-Z)
= (10 + 2Sqrt(169)) / (24i)
= (10 + 26) / 24i
= 36/(24i)
= 3/(2i)
= (3i) / (2i^2)
= -3i/2 #

 

[Trev]

[√(5+12i)+√(5-12i)]/[√(5+12i)-√(5-12i)]
Rationalising the denominator:
= [√(5+12i)+√(5-12i)]/[√(5+12i)-√(5-12i)] * [√(5+12i)+√(5-12i)]/[√(5+12i)+√(5-12i)]
= [(5+12i)+2√(25-144i²)+(5-12i)]/[5+12i-5+12i]
= [10+2.13]/[24i]
= 36/[24i]
=-3i/2
Hope there's not a mistake

 

[icycloud]

Hope there's not a mistake

Unless we both made the same mistake .