Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 3

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The common roots of the equations $z^{3} + (1 + i) z^{2} + (1 + i) z + i = 0$ , (where $i = \sqrt{- 1}$ ) and $z^{1993} + z^{1994} + 1 = 0$ are - (where $\omega$ denotes the complex cube root of unity).

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Important Questions on Complex Numbers

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 4

If

x_{r} = cis (\frac{π}{2^{r}})

for

1 \leq r \leq n; r, n \in N

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 5

Let

z_{1}, z_{2}

be two complex numbers represented by points on the circle

|z| = 1

and

|z| = 2

respectively, then

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 6

If

α, β

be any two complex numbers such that

|\frac{α - β}{1 - \bar{α} β}| = 1

, then which of the following may be true :

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 7

Let

z, ω z

and

z + ω z

represent three vertices of

∆ A B C

, where

ω

is cube root unity, then

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 8

Which of the following complex numbers lies along the angle bisectors of the lines
$L_{1} : z = (1 + 3 λ) + i (1 + 4 λ)$

$L_{2} : z = (1 + 3 μ) + i (1 - 4 μ)$

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 10

P (z)

be a variable point in the Argand plane such that

|z| = minimum \{|z - 1|, |z + 1|\},

then

z + z

will be equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 11

For two complex numbers

z_{1}

and

z_{2} : (a z_{1} + b {\bar{z}}_{1}) (c z_{2} + d {\bar{z}}_{2}) = (c z_{1} + d {\bar{z}}_{1}) (a z_{2} + b {\bar{z}}_{2})

if

(a, b, c, d \in R)

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 12

Which of the following locus of z on the complex plane represents a pair of straight lines?