Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 35

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If $z^{2} + z + 1 = 0,$ where $z$ is complex number, then the value of ${(z + \frac{1}{z})}^{2} + {(z^{2} + \frac{1}{z^{2}})}^{2} + {(z^{3} + \frac{1}{z^{3}})}^{2} + \dots \dots + {(z^{6} + \frac{1}{z^{6}})}^{2}$ is

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Important Questions on Complex Numbers

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 1

The value of

{(1 + i \sqrt{3})}^{6} + {(1 - i)}^{8}

is

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 2

A point

Z

moves on the curve

|Z - 4 - 3 i| = 2

in an argand plane. The maximum values of

|Z|

are

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 3

The points of intersection of the two curves

|Z - 3| = 2

and

|Z| = 2

in an Argand plane are

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 4

The solutions of the equation in $Z,$ ${|Z|}^{2} - (Z + \bar{Z}) + i (Z - \bar{Z}) + 2 = 0$ are

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 5

The solutions of the equation

(1 + i \sqrt{3})^{x} - 2^{x} = 0

form

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 6

A complex number

z

is such that

\arg (\frac{z - 2}{z + 2}) = \frac{π}{3}

. The points representing this complex number will lie on

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 7

Find 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

.

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 1>Q 8

If

z = r e^{i θ},

then

|e^{i z}|

equals