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Lesson Posted on 02 Feb Complex Numbers

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

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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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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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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What is the general equation of complex number?

K.vaishali .

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

Tapas Bhattacharya

Tutor

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

What is the value of i?

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

What inequality represents in complex number?

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