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Find the value of i-22 + i22 where i2 = -1

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Find the value of i-22 + i22 where i2 = -1
1. 1
2. i
3. -i
4. -2
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Correct Answer - Option 4 : -2

Concept:

The imaginary unit i is defined as i = √-1.

i4n + 1 = i, i4n + 2 = -1, i4n + 3 = -i, i4n = 1, etc.

Calculation:

Let z = i-22 + i22

= i-20 i-2 + i22i2

= (i4)-5 × (1/i2) + (i4)5 i2

= -1 - 1              (∵ i4n = 1)

= -2

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