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Lesson Posted on 02 Feb Complex Numbers

Raj Kumar

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We can think of complex numbers as vectors. Our aim in this section is to write complex numbers in terms of a distance from the origin and a direction (or angle) from the positive horizontal axis. We find the real (horizontal) and imaginary (vertical)... read more

We can think of complex numbers as vectors.

Our aim in this section is to write complex numbers in terms of a distance from the origin and a direction (or angle) from the positive horizontal axis.

We find the real (horizontal) and imaginary (vertical) components in terms of *r* (the length of the vector) and *θ* (the angle made with the real axis):

r2 = x2+y2

tanθ = y/x

x = rcosθ

y = rSinθ

Multiplying the last expression throughout by j(Imaginary number),

yj = jr sinθ

So we can write the polar form of a complex number as:

x+yj = r(cos θ+j sin θ)

*r* is the absolute value (or modulus) of the complex number

*θ* is the argument of the complex number.

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Comments Answered on 03/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

If [cube of (1 - i / 1 - i)] - [cube of (1 - i / 1 + i)] = x + iy, then the value of (x, y)?

Sarvajeet Kumar

An Experienced Trainer

(1,-1).

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Answers 1 Comments Answered on 03/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

If [square of (1 + i)] / 2 - i = x + iy, then find the value of x + y?

Sarvajeet Kumar

An Experienced Trainer

0.

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Answers 1 Comments Answered on 11/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

What is the general equation of complex number?

K.vaishali .

x + iy.

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Answers 1 Comments Answered on 30/11/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

What is the value of [square root of (-25)] * [square root of (-9)]?

Tapas Bhattacharya

Tutor

See the attachment:

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Answers 2 Comments Answered on 03/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

2 is a real number or imaginary number with respect to complex number?

Sarvajeet Kumar

An Experienced Trainer

A real number.

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Answers 1 Comments Asked on 04/11/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

For a positive integer n, find the value of [(1 - i) power n] [(1 - 1/i) power n]?

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Asked on 04/11/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

What is the formula for Argand plane with respect to complex number?

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Asked on 04/11/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Complex Numbers

What do you mean by real value and imaginary value with respect to complex number?

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What is the conjugate of 2 - i / [square of (1 - 2i)]?

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