The value of i592 - i590- i588 - i586 - i584i582 - i580 - i578 - i576 - i574 - 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 ...

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Standard XIII

Mathematics

Complex Numbers

The value of ...

Question

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

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Solution

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

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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}} + 2 =

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 =

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

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