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Complex Plane and Polar Form

Complex Plane and Polar Form

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Polar form


`a+ib``=r(cos theta+i sin theta)``=re^(itheta)`

Polar form of a Complex Number

plain and simple summary

nub

plain and simple summary

nub

dummy

Polar form of a complex number is `r (cos theta + i sin theta)`

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers, ordered pair of real numbers, are alternatively given by modulus and argument. This is the polar form of the complex number.


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Starting on learning "Polar Form of Complex Number". ;; Complex numbers, ordered pair of real numbers, are alternatively given by modulus and argument. This is the polar form of the complex number.

While introducing the generic form of complex numbers `a+i b`, it was discussed an equivalent form `r(cos theta + i sin theta)`. A quick revision of the same with complex plane is given here.

A number `a+b i` is equivalently given as `r(cos theta + i sin theta)` where `r = sqrt(a^2+b^2)` and `theta = tan^(-1)(b/a)`. polar form of complex number `r(cos theta + i sin theta)` is called the polar form or polar representation of the complex number.

What is the form of complex number given by `r (cos theta + sin theta)`?

  • Practice Saying the Answer

The answer is 'Polar form'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Polar Form: A number in the form `a+bi` is equivalently given as
`quad quad = r (cos (theta+ 2n pi) `
`quad quad quad quad + i sin (theta+ 2n pi))`
where `r = sqrt(a^2+b^2)`,
`theta = tan^(-1)(b/a)`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Convert `1+i` into polar form.

  • `2(cos(pi/4)+i sin(pi/4))`
  • `sqrt(2)(cos(pi/4)+i sin(pi/4))`
  • `cos(pi/4)+i sin(pi/4)`

The answer is '`sqrt(2)(cos(pi/4)+i sin(pi/4))`'

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Progress

While introducing the generic form of complex numbers a+i b, it was discussed an equivalent form r cos theta + i sine theta. A quick revision of the same with complex plane is given here.
A number a+b i is equivalently given as r cos theta + i sine theta; where r = square root a squared plus b squared ; and theta = tan inverse b by a.;; r cos theta + i sine theta is called the polar form or polar representation of the complex number.
Polar form of a complex number is r cos theta + i sine theta.
A number in the form a+b i is equivalently given as r cos theta plus 2 n pi + i sine theta plus 2 n pi; where r = square root a squared plus b squared ; and theta = tan inverse b by a.;;
What is the form of complex number given by r (cos theta + sine theta)?
polar
The answer is 'Polar form'.
C
2
2 cos pi by 4 + i sine pi by 4
square;root
square root 2 cos pi by 4 + i sine pi by 4
cos;cause
cos pi by 4 + i sine pi by 4
The answer is, square root 2 cos pi by 4 + i sine pi by 4

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