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Complex Numbers - Mathematics Questions asked by Filo students

Views: 5,251

\frac{( - 1 + i 3 ) ^{15}}{( 1 - i ) ^{20}} + \frac{( - 1 - i 3 ) ^{15}}{( 1 + i ) ^{20}}

- 64

- 32

- 16

\frac{1}{16}

Topic:

Complex numbers

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Views: 5,550

\frac{1 + 2 i}{1 + 3 i}

\frac{7}{10} - \frac{i}{10}

\frac{7}{10} + \frac{i}{10}

7 - i

\frac{7}{2} + \frac{i}{2}

Topic:

Complex numbers

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Views: 5,828

1 + i^{2} + i^{4} + i^{6} + \dots + i^{2 n}

= a. positive b. negative c. 0 d. cannot be determined

Topic:

Complex numbers

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Views: 5,984

\frac{( 1 + i ) ^{3}}{2 + i}

\frac{2}{5} - \frac{6}{5} i

- \frac{1}{5} + \frac{5}{6} i

- \frac{2}{5} + \frac{6}{5} i

Topic:

Complex numbers

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Views: 5,460

(2 - ω) (2 - ω^{2}) (2 - ω^{10}) (2 - ω^{11}) = \dots\dots ..

ω

is the complex cube root of unitya. 49 b. 50 c. 48 d. 47

Topic:

Complex numbers

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Views: 5,391

P

starts from the point

z_{0} = 1 + 2 i,

i = - 1

. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point

z_{1} ˙

z_{1}

the particle moves

2

units in the direction of the vector

\hat{i} + \hat{j}

and then it moves through an angle

\frac{π}{2}

in anticlockwise direction on a circle with centre at origin, to reach a point

z_{2} ˙

z_{2}

6 + 7 i

- 7 + 6 i

7 + 6 i

- 6 + 7 i

- 7 + 6 i

- 6 + 7 i

Topic:

Complex numbers

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Views: 5,958

A real value of

x

satisfies the equation

\frac{3 - 4 i x}{3 + 4 i x} = a - i b (a, b \in R), if a^{2} + b^{2} =

$1$
$- 1$
$2$
$- 2$

Topic:

Complex numbers

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Views: 5,269

A straight line is passing through thte points represented by the complex number a+ ib and

\frac{1}{- 1 + i b}

(a, b) \neq = (0, 0) .

Which one of the following is correct ?a. It passes thro ugh the origin b. It is parallel to the x-axis c. It is parallel to the y-axis d. It parallel to the y-axis

Topic:

Complex numbers

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Views: 5,238

All the points in the set

S = {\frac{α + i}{α - i} : α \in R} (i = - 1) l i e

on a a. cicle whose radius is

2

b. straight line whose slope is -1 c. circle whose radius is 1. d. straight line whose slope is 1.

Topic:

Complex numbers

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Question 10

Views: 5,708

Amplitude of the complex number

i sin (\frac{π}{19})

\frac{π}{19}

- \frac{π}{19}

\frac{π}{2}

\frac{π}{2} - \frac{π}{19}

Topic:

Complex numbers

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Question 11

Views: 5,677

a r g (\overline{z}) + a r g (- z) = {π, - π, if arg (z) < 0 if arg (z) > 0, where - π < a r g (z) \leq π

a r g (4 z_{1}) - a r g (5 z_{2}) = π, then ∣ ∣ \frac{z _{1}}{z _{2}} ∣ ∣

is equal to a. 1 b. 1.25 c. 1.5 d. 2.5

Topic:

Complex numbers

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Question 12

Views: 5,006

Assertion (A) : If 3 + iy is a root of

x^{2} + a x + b = 0

then a = -6
Reason (R) : If a, b , c are real and

Δ < 0

a x^{2} + b x + c = 0

are conjugate complex numbers a. Both A and R are true R is correct explanation to A b. Both A and R are true but R is not correct explanation of A c. A is true R is false d. A is false R is true

Topic:

Complex numbers

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Question 13

Views: 5,745

Complex conjugate of 3i-4 is:a.

3 i + 4

- 3 i - 4

- 3 i + 4

d. none of these

Topic:

Complex numbers

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Question 14

Views: 5,536

Convert the complex number

\frac{1}{( 1 + i )}

into polar form.

Topic:

Complex numbers

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Question 15

Views: 5,459

Evaluate the following if z = 5 -2i and w = -1 + 3i
2z + 3w

Topic:

Complex numbers

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Question 16

Views: 5,491

Evaluate the following if z = 5 -2i and w = -1 + 3i

(z + w)^{2}

Topic:

Complex numbers

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Question 17

Views: 5,734

Evaluate the followings :
(i)

i^{23}

i^{- 97}

Topic:

Complex numbers

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Question 18

Views: 5,184

(\frac{1}{2 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})

in the form of a +ib

Topic:

Complex numbers

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Question 19

Views: 5,460

\frac{13 i}{2 - 3 i}

A + B i

Topic:

Complex numbers

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Question 20

Views: 5,873

Express each of the complex number given in the exercise.

i^{- 39}

Topic:

Complex numbers

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