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summary of this topic

Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  argument of product is sum of arguments of multiplicand and multiplier.

    →  `arg (z_1 xx z_2) = arg(z_1) + arg(z_2)`

Argument in multiplication

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  argument of product is sum of arguments.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Argument of product is sum of arguments of the multiplicands.


Keep tapping on the content to continue learning.
Starting on learning "Argument in multiplication". ;; In this page you will learn Argument of product is sum of arguments of the multiplicands.

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`

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`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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 `

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

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Progress

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Progress

Given z1 = a1+i b1 and z2 = a2+i b2 what is the argument of product argument z1 multiplied z2?
multiplied
argument z1 multiplied argument z2
plus
argument z1 plus argument z2
The answer is 'argument z1 plus argument z2 '
Given z1 = a1+i b1 and z2 = a2+i b2, the argument of product ;; argument of z1 xx z2 ;; equals argument of r1 r2 e power i, theta1 + theta2 ;; equals theta1 + theta2 ;; equals argument of z1 + argument of z2
argument of product is sum of arguments.
Argument of Product: For complex numbers z1, z2 in CC ;; argument of z1 multiplied z2 = argument of z1 + argument of z2
Given z1 = a1+i b1 and z2 = a2+i b2, what is the argument of quotient argument z1 divided by z2?
divided
argument z1 divided argument z2
multiplied
argument z1 multiplied argument z2
minus
argument z1 minus argument z2
plus
argument z1 plus argument z2
The answer is 'argument z1 minus argument z2'

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