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Thought-Process to Discover Knowledge

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Complex numbers have additive inverse - negative of the number.



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What does 'inverse' mean?

  • same; identical; similar
  • opposite; converse
  • opposite; converse

The answer is 'opposite; converse'.

Consider two complex numbers `z_1 = a+ i b` and `z_2 = -a-ib`. What will be `z_1+z_2`?

  • `0+0i`
  • `0`
  • additive identity
  • All the above
  • All the above

The answer is 'All the above'. `-z` is called the additive inverse for `z` as `z+(-z) = 0`.

 •  For any complex number `z` there exits `-z` - additive inverse.

Additive Inverse: For any complex number `z = a+ib in CC`, there exists `-z = -a - i b in CC` such that
`z + (-z) = 0`

Solved Exercise Problem:

What is the additive inverse of `3.5+2.1i`?

  • `-3.5+2.1i`
  • `3.5-2.1i`
  • `-3.5-2.1i`
  • `0`

The answer is '`-3.5-2.1i`'

                            
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