Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 106

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If $ω = \cos \frac{π}{n} + i \sin \frac{π}{n},$ then value of $1 + ω + ω^{2} + \dots + ω^{n - 1}$ is

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Important Questions on Complex Numbers

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 107

The vertices of a triangle are

3 + 4 i, 4 + 3 i

and

2 \sqrt{6} + i,

then distance between ortho-centre and circum-centre of the triangle is equal to

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 108

The complex number

z

satisfying

z + |z| = 1 + 7 i,

then the value of

\sqrt{{|z + \bar{z}|}^{2} + {|z - \bar{z}|}^{2}}

is

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 109

If

z_{1}, z_{2}

and

z_{3}

are

3

distinct complex numbers such that

\frac{3}{|z_{1} - z_{2}|} = \frac{5}{|z_{2} - z_{3}|} = \frac{7}{|z_{3} - z_{1}|}

, then the value of

\frac{9}{z_{1} - z_{2}} + \frac{25}{z_{2} - z_{3}} + \frac{49}{z_{3} - z_{1}}

is equal to

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 110

The region of Argand diagram defined by

|z - 1| + |z + 1| \leq 4

is

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 111

For a complex number

Z

, if

Z = \frac{π}{4} {(1 + i)}^{4} (\frac{1 - \sqrt{π} i}{\sqrt{π} + i} + \frac{\sqrt{π} - i}{1 + \sqrt{π} i}),

then the value of

(\frac{|Z|}{amp (Z)})

is equal to (where

amp (Z) \in (- π, π]

)

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 112

If

z_{1} = 2 + 3 i, z_{2} = 3 - 2 i

and

z_{3} = - 1 - 2 \sqrt{3} i

, then which of the following is true? (where,

i^{2} = - 1

)

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 113

Let

|z_{1}| = 3, |z_{2}| = 2

and

z_{1} + z_{2} + z_{3} = 3 + 4 i

. If the real part of

(z_{1} \bar{z_{2}} + z_{2} \bar{z_{3}} + z_{3} \bar{z_{1}})

is equal to

4

, then

|z_{3}|

is equal to (where,

i^{2} = - 1

)

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Mathematics Crash Course MHT-CET>Chapter 8 - Complex Numbers>Exercise 1>Q 114

If

z_{i}

(where

i = 1, 2, \dots \dots \dots . . 6

) be the roots of the equation

z^{6} + z^{4} - 2 = 0

, then

\sum_{i = 1}^{6} {|z_{i}|}^{4}

is equal to