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Thought-Process to Discover Knowledge

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nub is the simple explanation of the concept.

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summary of this topic

Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Complex Multiplication is closed.

    →  `z_1 xx z_2 in CC`

Multiplication : Closure Law

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Product or quotient of two complex number is another complex number - closed

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is closed : Product or quotient of two complex number is another complex number


Keep tapping on the content to continue learning.
Starting on learning "Closure law of multiplication". ;; In this page you will learn that the product or quotient of two complex numbers is another complex number.

What does 'closure' mean?closure property illustration

  • closed
  • not open
  • both the above

Answer is 'both the above'

Given complex numbers `z_1=a_1+b_1i` and `z_2=a_2+b_2i`, `a_1,a_2,b_1,b_2 in R`, will `z_1 xx z_2` a complex number?

  • No. When multiplied, the result has `i^2`
  • Yes. When multiplied, the result consists of real numbers, as real and imaginary parts

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Closure property of Multiplication and Division: For any given complex numbers `z_1, z_2 in CC`, ` z_1 xx / -: z_2 in CC`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given complex numbers `z_1=a_1+b_1i` and `z_2=a_2+b_2i`, `a_1,a_2,b_1,b_2 in R`, will `z_1 -: z_2` a complex number?

  • No. Complex division is not defined
  • Yes. complex number division is equivalently multiplication by the conjugate

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

your progress details

Progress

About you

Progress

What does 'closure' mean?
closed;close
closed
not;open
not open
both;above
both the above
Answer is 'both the above'
Given complex numbers z1=a1+b1 i and z2=a2+b2 i, a1,a2,b1,b2 in real numbers, will z1 multiplied by z2 a complex number?
no;has;i;squared
No. When multiplied, the result has i squared
yes;s;consists;real;imaginary
Yes. When multiplied, the result consists of real numbers, as real and imaginary parts
The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'
Product or quotient of two complex number is another complex number - closed
Closure property of Multiplication and Division: For any given complex numbers z1, z2 in complex numbers, z1 multiplied or divided by z2 is a complex number
Given complex numbers z1=a1+b1 i and z2=a2+b2 i, a1,a2,b1,b2 in real numbers, will z1 divided by z2 a complex number?
no;not;defined
No. Complex division is not defined
yes;equivalently;multiplication;conjugate
Yes. complex number division is equivalently multiplication by the conjugate
The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

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