Question

product of 4th root of unity is

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Answer 1

Answer:

1,-1,i,-i

Step-by-step explanation:

consider z as the fourth root of unity

ie., z = (1)$\frac{1}{4}$

=> z⁴ = 1

=> z⁴ - 1 = 0

=> ($z^{2}$)² - ($1^{2}$)²   = 0

=> (z²+1) (z²-1) = 0

=> (z² - (-1) ) (z+1)(z-1) = 0

=> (z² - i² ) (z+1)(z-1)  = 0

=> (z+i)(z-i)(z+1)z-1)  = 0

so, z=1 , z=-1, z= i or z= -i