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If m, n, p, q are consecutive integers then the value of im ⋅ in ⋅ ip ⋅ iq is

If m, n, p, q are consecutive integers then the value of im ⋅ in ⋅ ip ⋅ iq is Correct Answer None of these

Concept:

i2 = -1, i4 = 1, i4n = 1 for all n ϵ z

Where z represents the whole number

Formula Used:

ax × ay = a(x + y)

Calculation:

According to the question

m, n, p and q are consecutive integers

We can express other integers as:

n = m + 1, p = m + 2 and q = m + 3

Now, We have to find the value of 

⇒ im × in × ip × iq

⇒ i(m + n + p + q)      (∵ ax × ay = a(x + y))

⇒ i

⇒ i(4m + 6)

⇒ i4m × i6

⇒ i4m × i4 × i2 

⇒ 1 × 1 × -1   

⇒ -1 

∴ The correct answer is option (4).

Mistake Points

Here we have to find im ⋅ in ⋅ ip ⋅ iq (terms are in product). ∴ The answer will be -1. If the terms were in summation, i.e. im + in + ip + iq form, then answer would have been zero.

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