Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 15

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If $z = (λ + 3) - i \sqrt{5 - λ^{2}},$ then the locus of $z$ is

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Important Questions on Complex Numbers

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 16

Let

z = 1 - t + i \sqrt{t^{2} + t + 2},

where

t

is a real parameter. The locus of

z

in the argand plane is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 17

If

z_{1} & z_{2}

are the complex roots of the equation

{(x - 3)}^{3} + 1 = 0,

then

z_{1} + z_{2}

equals to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 18

Which of the following is equal to

\sqrt[3]{- 1} ?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 19

If

x^{2} + x + 1 = 0,

then the value of

{(x + \frac{1}{x})}^{2} + {(x^{2} + \frac{1}{x^{2}})}^{2} + . . . + {(x^{27} + \frac{1}{x^{27}})}^{2} i s

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 20

Sum of the common roots of the equations

z^{3} + 2 z^{2} + 2 z + 1 = 0

and

z^{1985} + z^{100} + 1 = 0

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 21

If

5 x^{3} + M x + N where (M, N \in R)

is divisible by

x^{2} + x + 1,

then the value

M + N

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 22

If

z = x + i y & x^{2} + y^{2} = 16,

then the range of

||x| - |y|| is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 23

If

z

is a complex number satisfying the equation

z^{6} - 6 z^{3} + 25 = 0,

then the value of

|z|

is