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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsComplex NumbersComplex Plane and Polar Form

Complex Plane 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.



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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
  • 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.
  • 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 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 CC` 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. complex argand plane axes What is the axis on which real part `a` is shown as displacement on that axis?

  • imaginary axis
  • real 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
  • imaginary axis
  • real axis
  • 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.

Solved Exercise Problem:

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

  • `(-2,6)`
  • `(-2,6)`
  • `sqrt(2^2+6^2)`

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

                            
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