Question

evaluate 1÷i+1÷i^2+1÷i^3+1÷i^4 explain tell how the answer 0??​

Answer 1

Qᴜᴇsᴛɪᴏɴ

$\frac{1}{i} + \frac{1}{ {i}^{2} } + \frac{1}{ {i}^{3} } + \frac{1}{ {i}^{4} }$

Sᴏʟᴜᴛɪᴏɴ

As we know that

i= i or √-1

i² = -1

i³ = -i

i⁴ = 1

From here we got to know that

1 = i⁴, so replacing 1 by i⁴ in the given question we got

$\frac{ {i}^{4} }{i} + \frac{ {i}^{4} }{ {i}^{2} } + \frac{ {i}^{4} }{ {i}^{3} } + \frac{ {i}^{4} }{ {i}^{4} }$

Now cancelling the equivalent power of iota

i³ + i² +i + 1

Above we have already discussed about the values of different power of iota so here we will replace i by those values.

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

Hence proved..