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Thought-Process to Discover Knowledge

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mathsComplex NumbersComplex Plane and Polar Form

Modulus of a complex Number

Complex numbers are ordered pair of real numbers and a modulus is defined for that. This page explains the modulus of a complex number in detail.



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A Complex number `a+i b` is represented on complex plane as shown in the figure.modulus of complex number What is the length of the line segment between origin and the point represented by the complex number?

  • `sqrt(a^2+b^2)`
  • `sqrt(a^2+b^2)`
  • `a+i b`
  • `a+b`

The answer is '`sqrt(a^2+b^2)`'

The length of the line segment `OP` is called modulus of the complex number. It is represented as `|z|`modulus of complex number `|z|` is called modulus of z or mod z.

What does "modulus" mean?

  • absolute measure without any additional information
  • absolute measure without any additional information
  • mathematical model

The answer is 'absolute measure without any additional information'.

In complex number, the absolute measure of the number without splitting into the real or imaginary parts is modulus.

What is `|z|` called?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'Modulus or mod'.

The length of line segment from origin to the point represented by complex number is the modulus of the complex number.

Modulus: For a complex number `z=a+i b in CC`, the modulus of `z` is given as `|z| = sqrt(a^2+b^2)`

Solved Exercise Problem:

Find the modulus of `1.1-i`

  • `sqrt(0.21)`
  • `sqrt(2.21)`
  • `sqrt(2.21)`
  • `2.1`
  • `+-sqrt(2.21)`

The answer is '`sqrt(2.21)`'

                            
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