Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 48

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If all the three roots of $a z^{3} + b z^{2} + c z + d = 0$ have negative real parts $(a, b, c \in R)$ , then

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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 49

If

\frac{3}{2 + e^{i θ}} = a x + i b y

, then the locus of

P (x, y)

will represent

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

If

x = a + i b

is a complex number such that

x^{2} = 3 + 4 i & x^{3} = 2 + 11 i,

where

i = \sqrt{- 1}

then

(a + b)

is equal to

_______.

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

If the complex numbers

x

and

y

satisfy

x^{3} - y^{3} = 98 i

and

x - y = 7 i

, then

x y = a + i b

, where

a, b \in R

. The value of

(a + b)

equals

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

If

x = ω - ω^{2} - 2,

then the value of

x^{4} + 3 x^{3} + 2 x^{2} - 11 x - 6

is (where

ω

is cube root of unity)__________. Question Image

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

Let

z = 9 + b i,

where

b

is a non-zero real number and

i^{2} = - 1 .

If the imaginary part of

z^{2} & z^{3}

are equal, then

b

is _________.

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

Modulus of non-zero complex number

z

satisfying

\bar{z} + z = 0

and

{|z|}^{2} - 4 z i = z^{2}

is _______.

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 6

Modulus of non-zero complex number

z

satisfying

\bar{z} + z = 0

and

{|z|}^{2} - 4 z i = z^{2}

is _______.

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 7

If the expression

{(1 + i r)}^{3}

is of the form of

s (1 + i)

for some real number

s

, where

r

is also a real number, then sum of all possible values of

r

is ______.