Domain of 'fog'

Algebra Level 3

Domain of f ( g ( z ) ) f(g(z)) where f ( z ) = 1 z 2 − 1 f(z)=\frac{1}{z^{2}-1} and g ( z ) = 1 z g(z)= \frac{1}{z} is the set of Complex numbers except few of them.

Let P P be their product and S S be their sum. What is S + P + 1 S+P+1 ?


The answer is 1.

Zeeshan Ali by Zeeshan Ali , 25, Pakistan

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1 solution

展豪 張
Mar 20, 2016

The 'excepted' z z are z = 0 z=0 and ∣ z ∣ = 1 |z|=1 .
P = 0 P=0 , because of the 0 0 .
S = 0 S=0 , because ∣ z ∣ = 1 ⇔ ∣ − z ∣ = 1 |z|=1\Leftrightarrow|-z|=1 so they cancel out each other.
S + P + 1 = 1 S+P+1=1


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