Question

Find the value of i6+i7+i8+i9 /i2+i3

Answer 1

Answer:  The required value of the given expression is 0.

Step-by-step explanation:  We are given to find the value of the following expression involving the imaginary number i :

$E=\dfrac{i^6+i^7+i^8+i^9}{i^2+i^3}.$

We know that the value of the imaginary number is is given as

$i=\sqrt{-1},\\\\i^2=(\sqrt{-1})^2=-1,\\\\i^3=i\times(-1)=-i,\\\\i^4=(-1)^2=1,\\\\i^5=1\times i=i.$

Therefore, we get

$E\\\\\\=\dfrac{i^6+i^7+i^8+i^9}{i^2+i^3}\\\\\\=\dfrac{i^4(i^2+i^3+i^4+i^5)}{i^2+i^3}\\\\\\=\dfrac{1(-1+(-i)+1+i)}{-1-i}\\\\\\=\dfrac{-1-i+1+i}{-1-i}\\\\\\=\dfrac{0}{-1-i}\\\\=0.$

Thus, the required value of the given expression is 0.

Answer 2

Answer:

This is the solutionfor your given question

Thank you