Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 7

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Consider two complex numbers $z_{1}$ and $z_{2}$ such that $|z_{1} + z_{2}| = |z_{1}| - |z_{2}|,$ then the complex number $z = \frac{z_{1}}{z_{2}}$ will always lie on a

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Important Questions on Complex Numbers

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 8

The sum of the real roots of polynomial

72 - 36 z - 26 z^{2} + 13 z^{3} + 2 z^{4} - z^{5} = 0

will be

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 10

a, b, c

are real numbers in the polynomial

p (z) = 2 z^{4} + a z^{3} + b z^{2} + c z + 5 .

If two roots of the equation

p (z) = 0

are

2

and

i (= \sqrt{- 1}),

then the value of

a

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 11

Given that the equation

z^{2} + (a + i b) z + c + i d = 0

where

a, b, c, d

are non-zero, has a real root then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 13

If

x = - 5 + 2 \sqrt{- 4}

, then the value of the expression

x^{4} + 9 x^{3} + 35 x^{2} - x + 4

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 15

It is given that the equation

| z |^{2} - 2 i z + 2 α (λ + i) = 0

possesses a solution for all

α \in R,

then the number of integral value(s) of '

λ

' for which it is true is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 1

If

a, b, c

are real numbers and

z

is a complex number such that,

a^{2} + b^{2} + c^{2} = 1

and

b + i c = (1 + a) z

then

\frac{1 + i z}{1 - i z}

equals.

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 6

If

z_{1} = a + i b

and

z_{2} = c + i d

are complex numbers such that

|z_{1}| = |z_{2}| = 1

and

Re (z_{1} z_{2}) = 0

, then the pair of complex numbers

ω_{1} = a + i c

and

ω_{2} = b + i d

satisfies

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 8

If

Z_{1}, Z_{2}, Z_{3} \in C

such that

|Z_{1}| = |Z_{2}| = |Z_{3}| = 1

and

\frac{Z_{1}^{2}}{Z_{2} Z_{3}} + \frac{Z_{2}^{2}}{Z_{1} Z_{3}} + \frac{Z_{3}^{2}}{Z_{1} Z_{2}} + 1 = 0,

then the integral values that

|Z_{1} + Z_{2} + Z_{3}|

can attain, is