Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 11

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A point ' $z$ ' moves on the curve $| z - 4 - 3 i | = 2$ in an argand plane. The maximum and minimum values of $| z |$ are

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Important Questions on Complex Numbers

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 12

The set of points on the complex plane such that

z^{2} + z + 1

is real and positive (where

z = x + i y, x, y \in R

) is,

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 13

If

ω

is an imaginary cube root of unity, then

{(1 + ω - ω^{2})}^{7}

equals

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 14

If

i = \sqrt{- 1}

, then

4 + 5 {(- \frac{1}{2} + \frac{i \sqrt{3}}{2})}^{334} + 3 {(- \frac{1}{2} + \frac{i \sqrt{3}}{2})}^{365}

is equal to :

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 15

The set of points on an Argand plane which satisfy both

| z | \leq 4 &

\arg (z) = \frac{π}{3}

are lying on:

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 16

If arg

(z - 2 - 3 i) = \frac{π}{4},

then the locus of

z

is

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 17

The origin and the roots of the equation

z^{2} + p z + q = 0, p, q \in R

form an equilateral triangle in argand plane if -

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 18

If

z_{1}

and

z_{2}

are two non-zero complex numbers satisfying

|\frac{z_{1} - i z_{2}}{z_{1} + i z_{2}}| = 1

, then

\frac{z_{1}}{z_{2}}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-1>Q 19

{[\frac{- 1 + i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{6} + {[\frac{- 1 + i \sqrt{3}}{2}]}^{5} + {[\frac{- 1 - i \sqrt{3}}{2}]}^{5}

is equal to