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Thought-Process to Discover Knowledge

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

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nub is the simple explanation of the concept.

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Complex Plane and Polar Form

Complex Plane and Polar Form

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Complex Plane


 »  Real line extended to complex plane
    →  Argand Plane


 »  Complex plane for `a+ib`

    →  real part `a` on real-axis or real-line

    →  imaginary part `b` on imaginary-axis

    →  coordinate equivalent `(a,b)`

Complex Plane or Argand Plane

plain and simple summary

nub

plain and simple summary

nub

dummy

A complex plane or Argand plane is a 2D plane with complex numbers assigned as points in the plane.

The axes in complex plane are real axis and imaginary axis.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex number `a+i b` is equivalently an ordered pair `(a,b)` which can be abstracted to represent a 2D plane called Argand Plane or Complex Plane.


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Starting on learning "Complex or Argand Plane". ;; Complex number a+i b is equivalently an ordered pair; a,b ; which can be abstracted to represent a 2D plane, called Argand Plane, or, complex plane.

Consider the plane with `x`-axis and `y`-axis, where a ordered pair of `(a,b)` is represented with a point on the plane. What is this plane called?

  • 2D Cartesian Plane
  • No such plane is defined

The answer is '2D Cartesian Plane'.

The complex number representation is simplified to the form `a+i b`. Can this be considered as a ordered pair?

  • No, as `a+i b` has imaginary part.
  • Yes, as the numbers `a,b` are real numbers.

The answer is 'Yes, as the numbers `a,b` are real numbers.'

Similarity between points in 2D Cartesian plane and the complex numbers leads to definition of Complex plane.complex argand plane illustration The complex plane is also called Argand plane named after the French Mathematician J R Argand.

A Complex number `a+i b` is represented on complex plane as shown in the figure. complex argand plane axes What is the axis on which real part `a` is shown as displacement on that axis?

  • imaginary axis
  • real axis
  • complex axis

The answer is 'real axis'

A Complex number `a+i b` is represented on complex plane as shown in the figure.complex argand plane axes What is the axis on which imaginary part `b` is shown as displacement on that axis?

  • imaginary axis
  • real axis
  • complex axis

The answer is 'imaginary axis'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Complex Plane or Argand Plane: A 2D plane in which a complex number `a+i b in CC` is assigned to a point `(a, b)` as displacements along two axes of the plane.

Real and Imaginary Axes: In the complex plane, the axis on which real part of complex numbers are mapped is called the real axis and the other axis on which the imaginary part of complex numbers are mapped is called the imaginary axis.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is the point corresponding to the complex number `-2+i6` on the Argand plane?

  • `(-2,6)`
  • `sqrt(2^2+6^2)`

The answer is '`(-2,6)`'

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Progress

About you

Progress

Consider the plane with x -axis and y -axis, where a ordered pair of (a,b) is represented with a point on the plane. What is this plane called?
Cartesian;2;d
2D Cartesian Plane
no;such;defined
No such plane is defined
The answer is '2D Cartesian Plane'.
The complex number representation is simplified to the form a+i b . Can this be considered as a ordered pair?
no;not;imaginary;part
No, as a+i b has imaginary part.
yes;real
Yes, as the numbers a,b are real numbers.
The answer is 'Yes, as the numbers a,b are real numbers.'
Similarity between, points in 2D Cartesian plane, and the complex numbers, leads to definition of Complex plane. ;; The complex plane is also called Argand plane named after the French Mathematician J R Argand.
A complex plane or Argand plane is a 2D plane, with, complex numbers assigned as points in the plane.
Complex Plane or Argand Plane: A 2D plane in which a complex number a+i b, in set of complex numbers, is assigned to a point (a, b) as displacements along two axes of the plane.
A Complex number a+i b is represented on complex plane as shown in the figure. What is the axis on which real part a is shown as displacement on that axis?
imaginary
imaginary axis
real
real axis
complex
complex axis
The answer is 'real axis'
A Complex number a+i b is represented on complex plane as shown in the figure. What is the axis on which imaginary part b is shown as displacement on that axis?
imaginary
imaginary axis
real
real axis
complex
complex axis
The answer is 'imaginary axis'
The axes in complex plane are real axis and imaginary axis.
Real and Imaginary Axes: In the complex plane, the axis on which real part of complex numbers are mapped, is called the real axis ;; and the other axis on which the imaginary part of complex numbers are mapped, is called the imaginary axis.
What is the point corresponding to the complex number minus 2+i6 on the Argand plane?
2 6;minus
minus 2 six
square;root;plus;squared
square root 2 squared plus six squared
The answer is "minus 2 6".

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