Question

find the value of i^23+i^24+i^25+i^26.

Answer 1

i^23+i^24+i^25+i^26
=i^[(4*5)+3]+i^(4*6)+i^[(4*6)+1]+i^[(4*6)+2]
=i^ 3+i^0+i^1+i^2
=-i+1+i-1
=0

Answer 2

Concept :

The numbers which are expressed in the form of $a+ib$ are called complex numbers. In which iota $(i)$ is an imaginary number.

Given :

We have given the equation $i^{23}+i^{24}+i^{25}+i^{26}$.

Solution :

Consider the equation $i^{23}+i^{24}+i^{25}+i^{26} ...(1)$      

We know that according to the definition of iota

$i^2=-1$,  

$i^3=-i$,

and $i^4=1$

Now, the equation $1$ can be written as :

$-i+1+i-1=0$

Hence, the correct answer is $0$.

#SPJ2