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

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IMPORTANT

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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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Important Questions on Complex Numbers

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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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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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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

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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

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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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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

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

If

z

is non-real and

i = \sqrt{- 1},

then

\sin^{- 1} (\frac{1}{i} (z - 1))

be the angle of a triangle, if

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Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 3

If

|z_{1}| = |z_{2}| = \dots \dots |z_{n}| = 1,

then the value of

|z_{1} + z_{2} + \dots \dots z_{n}| - |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \dots \dots + \frac{1}{z_{n}}|

is