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Lesson Posted on 02/02/2018 Learn Complex Numbers

Polar Form Of Complex Number

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.

                                                 Complex number on the complex plane

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

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

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

Sarvajeet Kumar

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0.
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Answered on 11/12/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

What is the general equation of complex number?

K.vaishali .

x + iy.
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Answered on 30/11/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

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

Tapas Bhattacharya

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See the attachment:
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Answered on 03/12/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

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

Sarvajeet Kumar

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A real number.
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Asked on 04/11/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

If z = x + iy, then show that z * (bar of z) + 2 (z + bar of z) + b = 0, where b belongs to R, represents a circle?

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Asked on 04/11/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

Show that the complex number z, satisfying the condition arg (z - 1 / z + 1) = ? / 4 lies on a circle? Solve... read more
Show that the complex number z, satisfying the condition arg (z - 1 / z + 1) = ? / 4 lies on a circle? Solve the equation (modulus of z) = z + 2i? read less

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Asked on 04/11/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

If [modulus of (z + 1)] = z + 1 + 2i, then find z?

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Asked on 04/11/2016 Learn Complex Numbers +2 Class XI-XII Tuition (PUC) Mathematics

Fill in the blank: For any two complex numbers z1, z2 and any real numbers a, b, {square of } + {square of } = _____? read more
Fill in the blank: For any two complex numbers z1, z2 and any real numbers a, b, {square of [modulus of (az1 - bz2)]} + {square of [modulus of (bz1 + az2)]} = _____? read less

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