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Answer :
Final answer:
The Euler phi function gives the count of positive integers less than or equal to n that are relatively prime to n. For ϕ(20000), the value is 8000. The absolute values of z and u are 20000 and 19999, respectively.
Explanation:
The Euler phi function, denoted as ϕ(n), gives the count of positive integers less than or equal to n that are relatively prime to n. In other words, ϕ(n) is the number of positive integers that do not share any common factors with n (except for 1).
Given the formula for the Euler phi function, we can find that ϕ(20000) = 8000.
For part (b), ∣z₂₀₀₀₀∣ refers to the absolute value of z and ∣u₂₀₀₀₀∣ refers to the absolute value of u. The given options state that ∣z₂₀₀₀∣ = 20000 and ∣u₂₀₀₀∣ = 19999.
Therefore, the correct option is a)ϕ(20000)=8000, ∣z₂₀₀₀∣=20000, ∣u₂₀₀₀∣=19999.
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