Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 29

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If $|z_{1}| = 2$ and $(1 - i) z_{2} + (1 + i) {\bar{z}}_{2} = 8 \sqrt{2}$ , then the minimum value of $|z_{1} - z_{2}|$ is _____ units.

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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 30

Given that

1 + 2 {|z|}^{2} = {|z^{2} + 1|}^{2} + 2 {|z + 1|}^{2}

, then the value of

|z (z + 1)|

is_.

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Archives>Q 1

If

|z - \frac{4}{z}| = 2,

then the maximum value of

|z|

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Archives>Q 2

The number of complex numbers

z

such that

| z - 1 | = | z + 1 | = | z - i |

equals

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

Let

α, β

be real and

z

be a complex number. If

z^{2} + α z + β = 0

has two distinct roots on the line

Re z = 1,

then it is necessary that

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Archives>Q 4

If

ω (\neq 1)

is a cube root of unity and

(1 + ω)^{7} = A + B ω .

Then,

(A, B)

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Archives>Q 5

If

z \neq 1

and

\frac{z^{2}}{z - 1}

is real, then the point represented by the complex number

z

lies

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Permutation and Combination>Archives>Q 6

If

z

is a complex number of unit modulus and argument

θ,

then

a r g (\frac{1 + z}{1 + \bar{z}})

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Permutation and Combination>Archives>Q 7

If $z$ a complex number such that $|z| \geq 2$ , then the minimum value of $|z + \frac{1}{2}|$