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Thought-Process to Discover Knowledge

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Argument of product is sum of arguments of the multiplicands.



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Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2` what is the argument of product `text(arg)(z_1 xx z_2)`?

  • `text(arg)z_1 xx text(arg)z_2`
  • `text(arg)z_1 + text(arg)z_2`
  • `text(arg)z_1 + text(arg)z_2`

The answer is '``text(arg)z_1 + text(arg)z_2``'.

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2`, the argument of product
`text(arg)(z_1 xx z_2)`
`quad quad = text(arg)(r_1r_2 e^(i theta_1 + theta_2))`
`quad quad = theta_1 + theta_2`
`quad quad = text(arg)z_1 + text(arg)z_2`

 •  argument of product is sum of arguments.

Argument of Product: For complex numbers `z_1, z_2 in CC`
`text(arg)(z_1 xx z_2) = text(arg)z_1 + text(arg)z_2`

Solved Exercise Problem:

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2`, what is the argument of quotient `text(arg)(z_1 -: z_2)`?

  • `text(arg)z_1 -: text(arg)z_2`
  • `text(arg)z_1 xx text(arg)z_2 `
  • `text(arg)z_1 - text(arg)z_2 `
  • `text(arg)z_1 - text(arg)z_2 `
  • `text(arg)z_1 + text(arg)z_2 `

The answer is '`text(arg)z_1 - text(arg)z_2`'.

                            
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