a)z2 = 1 b)z3 = 1 c)z4 = 1 d)z9 = 1Correct answer is option 'C'. C...
Explanation:
To solve this question, we need to substitute z3 with z and then check which of the given options satisfy the equation.
Let's go through each option and substitute z3 with z:
a) z2 = 1:
Substituting z3 with z, we get (z)2 = 1.
By simplifying, we have z2 = 1.
This is a quadratic equation, and it does not match the given equation.
Hence, option 'a' is not the correct answer.
b) z3 = 1:
Substituting z3 with z, we get (z)3 = 1.
By simplifying, we have z3 = 1, which is the given equation.
Therefore, option 'b' is a possible solution.
c) z4 = 1:
Substituting z3 with z, we get (z)4 = 1.
By simplifying, we have z4 = 1.
This equation does not match the given equation z3 = 1.
Hence, option 'c' is not the correct answer.
d) z9 = 1:
Substituting z3 with z, we get (z)9 = 1.
By simplifying, we have z9 = 1.
This equation does not match the given equation z3 = 1.
Hence, option 'd' is not the correct answer.
Therefore, the correct answer is option 'b' as it satisfies the given equation z3 = 1.