A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 14

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JEE Main Paper 2A- B.Arch

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$z_{1}$ and $z_{2}$ are unimodular complex number that satisfy $z_{1}^{2} + z_{2}^{2} = 4$ , then ${(z_{1} + {\bar{z}}_{1})}^{2} + {(z_{2} + {\bar{z}}_{2})}^{2}$ is equal to

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Important Questions on Complex Numbers and Quadratic Equations

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 15

The complex number

z

satisfying

| z + \bar{z} | + | z - \bar{z} | = 2

and

| i z - 1 | + | z - i | = 2

is/are

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 16

The number of real solutions of the equation

|x^{2} + 4 x + 3| + 2 x + 5 = 0

are

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 17

The equation

(\cos β - 1) x^{2} + (\cos β) x + \sin β = 0

in the variable

x

has real roots, then

β

is in the interval.

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 18

If

x^{2} + 5 = 2 x - 4 \cos (a + b)

, where

a, b \in (0, 5)

, is satisfied for atleast one real

x,

then the maximum value of

a + b

in

[0, 2 π]

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 19

The set of value of

' a'

for which

1

lies between the roots of equation

x^{2} - a x - a + 3 = 0

is

EASY

JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 11 - Complex Numbers and Quadratic Equations>EXERCISE>Q 20

The value of

|a|

for which

\sin θ

and

cosec θ

are the roots of the equation

x^{2} + a x + b = 0

is