If the fourth roots of unity are A,B,C,D then $A^{2} + B^{2} + C^{2} + D^{2}$ is equal to

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None of these

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Solution

The correct option is A 1
Fourth root of unity are
$1, - 1, c, - c$
$A^{2} + B^{2} + C^{2} + D^{2}$
$(1)^{2} + (- 1)^{2} + (i)^{2} + (- i)^{2}$
$1 + 1 + i^{2} + i^{2}$
$1 + 1 - 1 - 1$
$0$

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