Question 1205500
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z*conj(z) = |z|^2
z*conj(z) = 8^2
z*conj(z) = 64
conj(z) = 64/z


Apply substitution and simplify.
(conj(z) + 48)/(3z+4)
= (64/z + 48)/(3z+4)
= (64 + 48z)/(z(3z+4)) ... multiply top and bottom by z
= (16(3z+4))/(z(3z+4))
= 16/z
We have something much more simple to work with.


Which means,
| (conj(z) + 48)/(3z+4) |
= | 16/z |
= |16| / |z|
= 16/8
= <font color=red>2</font>


Therefore, | (conj(z) + 48)/(3z+4) | = <font color=red size=4>2</font> when |z| = 8
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