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Thought-Process to Discover Knowledge

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mathsComplex NumbersAlgebra of Complex Numbers

Equivalence of complex numbers

When two complex numbers are considered to be equal?

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When will two complex numbers `z_1=a+ib` and `z_2=p+iq` be equal?

  • when modulus are equal `|z_1| = |z_2|`
  • when argument are equal `text(arg)z_1 = text(arg)z_2`
  • when real and imaginary parts are equal `a=p` and `b=q`
  • when real and imaginary parts are equal `a=p` and `b=q`
  • when real or imaginary parts are equal `a=p` or `b=q`

The answer is 'if real and imaginary parts are equal `a=p` and `b=q`'

Two complex numbers are equal if real and imaginary parts are equal.

Complex numbers Equivalence: Two complex numbers `z_1=a_1+ib_1` and `z_2=a_2+ib_2` are equal only if `a_1=a_2` and `b_1=b_2`

Solved Exercise Problem:

If two complex numbers `3-i4` and `1+x` are equal, What is x?

  • `-4`
  • `2-i4`
  • `2-i4`
  • `3-i4`
  • `-4i`

The answer is '`2-i4`'

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