Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

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Important Questions on Waves

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

For all complex numbers

z

of the form

1 + i α, α \in R,

if

z^{2} = x + i y,

then

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The value of sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1}), where i = \sqrt{- 1},

equals

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If

x + i y = \sqrt{\frac{2 + i}{2 - i}}

, then

x^{2} + y^{2}

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The value of ${(1 + i)}^{5} \times {(1 - i)}^{5}$ is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If

a = \cos θ + i \sin θ

, then

\frac{1 + a}{1 - a}

is equal to

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

For any value of

t

,

(\cos t + i \sin t) (\cos t - i \sin t)

is given by

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The conjugate of complex number

\frac{2 - 3 i}{4 - i}

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The value of $5 i^{5} + 4 i^{4} - 3 i^{3} + 2 i^{2} - i$ is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The range of real number

α

for which the equation

z + α |z - 1| + 2 i = 0

has a solution is -

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The additive inverse of

1 - i

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The value of

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

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If

z_{1}, z_{2} & z_{3}

are the complex numbers, such that

|z_{1}| = |z_{2}| = |z_{3}| = |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}}| = 1

, then

|z_{1} + z_{2} + z_{3}|

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If the multiplicative inverse of

\frac{(i + 1) (i + 2)}{(i - 1) (i - 2)} = \frac{k + m i}{l}

(lowest form), then

k + m + l =

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The smallest positive integer

n

for which

{(\frac{1 + i}{1 - i})}^{n} = 1

, is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The multiplicative inverse of the complex number

(a, b)

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If

f (x) = (\cos x + i \sin x) (\cos 3 x + i \sin 3 x) \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \{\cos (2 n - 1) x + i \sin (2 n - 1) x\}

, then

f^{"} (x)

is

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The locus of

z

satisfying the inequality

\log_{(0.8)} |z + 1| > \log_{(0.8)} |z - 1|

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If

{(\frac{1 + i}{1 - i})}^{x} = 1

, then

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Cotyledons are also called-

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Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The number of solutions of the equation

z^{2} + \bar{z} = 0

is -