Question

The value of i³ + i⁶ + i⁹, where \({\rm{i}} = \sqrt { - 1} \), is
1. 1
2. -1
3. i
4. -i

Answer 1

Correct Answer - Option 2 : -1

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 + i6 + i9

As we know, i2 = -1

So,i3 =  i2 × i= -1 × i = -i

i6 = i3 × i3 = -i × -i = i² = -1

i⁹ = i3 × i3 × i3  = -i × -i × -i = -i³ = -(-i) = i 

Now,

i3 + i6 + i9 = (-i) + (-1) + i = -1