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The value of i3 + i4 + i5, where \({\rm{i}} = \sqrt { - 1} \), is

  1. 1
  2. 0
  3. i
  4. -1

Answer (Detailed Solution Below)

Option 1 : 1
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Detailed Solution

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Concept:

Power of i:

  • i = \(\sqrt{-1}\)
  • i2 = -1
  • i3 = -i × i2 = -i
  • i4 = (i2)2 = (-1)2 = 1
  • i4n = 1

 

Calculation:

To Find: Value of i3 + i4 + i5

As we know, i2 = -1

So, i3 = -i × i2 = -i

i4 = (i2)2 = (-1)2 = 1

i5 = i4 × i = 1 × i = i

Now,

i3 + i4 + i 5 = -i + 1 + i = 1

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Last updated on Apr 28, 2025

-> The Indian Army has released the official notification for the post of Indian Army Havildar SAC (Surveyor Automated Cartographer).

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

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