Complex NumbersHard

Question

The value of sum (in + in + 1), where i = √-1 equals

Options

A.i
B.i - 1
C.-i
D.0

Solution

     (in + in + 1) = in(1 + i) = (1 + i) in
= (1 + i) = (1+ i2 + i3 + ......+ i13) = (1 + i)
= (1+ i)i = -1+ i
Alternate Solution
Since, sum of any four consecutive powers of iota is zero.
∴ (in + in+1) = (i + i2 + ...... + i13)
+ (i2 + i3+ .......+i14) = i + i13 + ......+ i14

Create a free account to view solution

View Solution Free
Topic: Complex Numbers·Practice all Complex Numbers questions

More Complex Numbers Questions

If z1, z2 ∈ C, then which statement is true ?...If | z | = 3, then point represented by 2 − z lie on the circle -...If (1 + i) (1 + 2i) ( 1 + 3i) .... (1 + ni) = α + iβ then 2 . 5. 10 .... (1 + n2) =...The locus of z which lies in shaded region is best represented by...The value of z for which | z + i | = | z − i | is-...