Question

Two square roots of the unity are

A) 1, -1

B) -1, $\omega$

C) 1, $- \omega$

D) $i,{i^2}$

Answer 1

Hint : In this question, we need to evaluate the square roots of the unity term. For this, we will first define the term unity and then, impose the square root on it. In math’s unity there are simple synonyms of the number one ‘1’, in this question we need to find the square roots of the number ‘1’.

Complete step-by-step answer :

Here Unity refers to 1 and we need to find the square roots of 1

We know the square root of a number is represented as: $\sqrt {{a^2}} = \pm {a^{ \left( {2 \times \dfrac{1}{2}} \right)}} = \pm a$

So we can write the square root of $\sqrt 1 = \pm 1$ , since the value of square number 1 is 1 only.

Hence the two square roots of the unity are -1, 1

To verify:-

Since we know when a square root of a number is multiplied by itself then it gives the original number so we will multiply both the roots by it to verify the answer

When root is 1,

$\Rightarrow { \left( 1 \right)^2} = 1 \times 1$

$= 1$

=Unity

When the root is -1,

$\Rightarrow { \left( { - 1} \right)^2} = \left( { - 1} \right) \times \left( { - 1} \right)$

$= + 1$

= Unity

Hence verified the square roots of unity is -1, 1

So, the correct answer is “Option A”.

Note : It is interesting to note here that the square root of the positive term always yields one positive and one negative number. We know the square root of a number is a value that when multiplied together gives the original number and in this case the original number is ‘1’.