The value of i 592- i 590- i 588- i 586- i 584- i 582- i 580- i 578- i 576- i 574-2-

Given: i^592 + i^590 + i^588 + i^586 + i^584i^582 + i^580 + i^578 + i^576 + i^574 + 2 We know i^4n=1 and nbsp;i^4n+2= 1 (i^4)^148 + (i^4)^147.i^2 +(i^4)^147 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Complex Numbers

The value of ...

Question

The value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} + 2 =$

Open in App

Solution

We know $i^{4 n} = 1$ and $i^{4 n + 2} = - 1$
$\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} + 2$
$= \frac{1 + (- 1) + 1 + (- 1) + 1}{(- 1) + 1 + (- 1) + 1 + (- 1)} + 2$
$= - 1 + 2 = 1$

Suggest Corrections

Similar questions

Q. Solve :-

\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}

Q. The value of

\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1

is
(a) −1
(b) −2
(c) −3
(d) −4

The value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}$ - 1 =

Q. Find the values of the following expressions:
(i) i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰
(ii) i³⁰ + i⁸⁰ + i¹²⁰
(iii) i + i² + i³ + i⁴
(iv) i⁵ + i¹⁰ + i¹⁵
(v)

\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}

(vi) 1+ i² + i⁴ + i⁶ + i⁸ + ... + i²⁰
(vii) (1 + i)⁶ + (1 − i)³

The value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}$ -1 is

Join BYJU'S Learning Program

Explore more

Complex Numbers

Standard XII Mathematics

Join BYJU'S Learning Program

The value of i592+i590+i588+i586+i584i582+i580+i578+i576+i574+2=

We know i4n=1 and i4n+2=−1 i592+i590+i588+i586+i584i582+i580+i578+i576+i574+2 =1+(−1)+1+(−1)+1(−1)+1+(−1)+1+(−1)+2 =−1+2=1

The value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} + 2 =$

We know $i^{4 n} = 1$ and $i^{4 n + 2} = - 1$
$\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} + 2$
$= \frac{1 + (- 1) + 1 + (- 1) + 1}{(- 1) + 1 + (- 1) + 1 + (- 1)} + 2$
$= - 1 + 2 = 1$