Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 29

MEDIUM

JEE Main

IMPORTANT

Earn 100

The sum of $162^{t h}$ power of the roots of the equation $x^{3} - 2 x^{2} + 2 x - 1 = 0$ is ______.

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Important Questions on Complex Numbers

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 30

The equation

z \bar{z} + (2 - 3 i) z + (2 + 3 i) \bar{z} + 4 = 0

represents a circle of radius

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 31

A regular hexagon is drawn with two of its vertices forming a shorter diagonal at

z = - 2

and

z = 1 - i \sqrt{3} .

The other four vertices are

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 32

z_{1}, z_{2}, z_{3}

are the affixes of the vertices of a triangle having it circumcentre at the origin. If

z

is the affix of its orthocentre, then

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 33

If the complex numbers $z_{1}, z_{2}$ and $z_{3}$ are in $A . P .,$ then they lie on a

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 34

If

\frac{|z - 2|}{|z - 3|} = 2

represents a circle, then its radius is

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 35

If a complex number

z

lies on a circle of radius

3

and centre at

z_{0} = 0

then the complex number

(- 3 + 9 z)

lies on a circle of radius

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 36

If

z_{1}, z_{2}, z_{3}

are vertices of an equilateral triangle with orthocentre

z_{0}

then

z_{1}^{2} + z_{2}^{2} + z_{3}^{2} = k z_{0}^{2}

, where

k \in N

, then

k

is equal to

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 1

If the area of the triangle on the complex plane formed by the

3

points

z, z + i z

and

i z

is

200,

then the value of

3 |z|

must be equal to