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Parallelogram

Identify the ...

Question

Identify the correct relations with respect to the given parallelogram.

A

∠1 = ∠4

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B

∠1 = ∠5

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C

∠6 = ∠5

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D

∠6 = ∠2

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E

∠1 = ∠2

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F

∠4 = ∠3

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G

DO = OB

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H

AO = OC

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I

AB = DC

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J

AD = BC

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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

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

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

Identify the correct relations with respect to the given parallelogram.

The value of $i^{586}$ is

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