Question

1/i + 1/i^2 + 1/i^3 + 1/i^4 :::express in the form of b or bi ,where b is a real number.​

Answer 1

Answer:

$\frac{1}{i} + \frac{1}{ {i}^{2} } + \frac{1}{ {i}^{3} } + \frac{1}{ {i}^{4} } \\ = \frac{1}{i} + \frac{1} { -1} + \frac{1}{ {i}^{2} \times i} + \frac{1}{ {i}^{2} \times {i}^{2} } \\ = \frac{1}{i} - 1 + \frac{1}{ ( - 1) \times i} + \frac{1}{ (- 1) \times ( - 1) } \\ = \frac{1}{i} - 1 - \frac{1}{i} + 1 = 0 + 0i \\ \: which \: is \: in \: the \: form \: of \: a + bi \\ a = 0 \: and \: b \: = 0$

i^2 = - 1