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Thought-Process to Discover Knowledge

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mathsComplex NumbersProperties of Complex Number Arithmetic

### Argument in multiplication

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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