Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 42

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Let $z_{1}$ and $z_{2}$ are two complex numbers such that $(1 - i) z_{1} = 2 z_{2}$ and arg $(z_{1} z_{2}) = \frac{π}{2},$ then arg $(z_{2})$ is equal to

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Important Questions on Complex Numbers

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 43

If

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

(where

z_{1}

and

z_{2}

are non-zero complex numbers), then

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 44

a, b, c

are real numbers in the polynomial,

P (z) = 2 z^{4} + a z^{3} + b z^{2} + c z + 3 .

If two roots of the equation

P (z) = 0

are

2

and

i

. Then which of the following are true.

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 45

If

z = \frac{(1 + i) (1 + 2 i) (1 + 3 i) \dots \dots (1 + n i)}{(1 - i) (2 - i) (3 - i) \dots . . (n - i)}, n \in N

, then principal argument of

z

can be

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 46

For complex numbers

z

and

w

, if

{|z|}^{2} w - {|w|}^{2} z = z - w

. Which of the following are true?

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 47

If

z

satisfies the inequality

|z - 1 - 2 i| \leq 1,

then which of the following are true

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 48

The curve represented by

z = \frac{3}{2 + \cos θ + i \sin θ}, θ \in [0, 2 π] .

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 49

P O Q

is a straight line through the origin

O, P

, and

Q

represent the complex number

a + i b

and

c + i d

, respectively, and

O P = O Q

. Then which of the following are true?

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 50

Let

i = \sqrt{- 1} .

Define a sequence of complex number by

z_{1} = 0, z_{n + 1} = {z_{n}}^{2} + i

for

n \geq 1 .

Then which of the following are true.