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Thought-Process to Discover Knowledge

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

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User Guide    

nub is the simple explanation of the concept.

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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Complex number multiplication


 »  `(a+ib) xx (c+id)`
by associative, commutative, distributive laws of real numbers, considering `i` as a variable, and applying `i^2=-1`
    →  `=(ac-bd) + i(cb+ad)`

Multiplication of two Complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Multiplication of two complex numbers follows numerical expression laws and properties with `sqrt(-1)` handled as per the property `(sqrt(-1))^2 = -1`

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers multiplication is explained.


Keep tapping on the content to continue learning.
Starting on learning "Multiplication of two complex numbers". ;; In this page, complex numbers multiplication is explained.

Consider two complex numbers `z_1=a_1+ib_1` and `z_2 = a_2+ib_2`. What is `z_1 xx z_2`?

  • `(a_1a_2-b_1b_2) + i (a_2b_1+a_1b_2)`
  • `a_1a_2+ib_1b_2`
  • `(a_1a_2+b_1b_2)+i(a_1b_2+a_2b_1)`

The answer is '`(a_1a_2-b_1b_2) + i (a_2b_1+a_1b_2)`'. This is from the associative and distributive laws of real numbers extended to numbers with `sqrt(-1)`.

`z_1=a_1+ib_1` and `z_2 = a_2+ib_2`. What is `z_1 xx z_2`?
Solution :
`z_3 = z_1 xx z_2 `
`quad quad = (a_1+ib_1)xx(a_2+ib_2)`
`quad quad = a_1 xx(a_2+ib_2)`
`quad quad quad quad +i b_1xx (a_2+ib_2) `
`quad quad = a_1a_2+ia_1b_2+ib_1a_2`
`quad quad quad quad +i^2b_1b_2`
`quad quad = (a_1a_2-b_1b_2) `
`quad quad quad quad + i(b_1a_2+a_1b_2)`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Multiplication of two complex numbers : For any complex number `z_1=a_1+ib_1 in CC` and `z_2 = a_2+ib_2 in CC`
`z_1 xx z_2 = (a_1a_2-b_1b_2)`
`quad quad quad quad quad +i(a_2b_1+a_1b_2)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `z_1=1+2i` and `z_2=3-i` what is `z_1 xx z_2`?

  • `5+5i`
  • `-5+5i`
  • `5-5i`
  • `-5-5i`

The answer is '`5+5i`'

your progress details

Progress

About you

Progress

Consider two complex numbers z 1=a 1+i b 1 and z 2 = a 2+i b 2 . What is z 1 multiplied by z 2 ?
option 1
a 1 a 2 minus b 1 b 2 + i a 2 b 1+a 1 b 2
option 2
a 1 a 2+i b 1 b 2
option 3
a 1 a 2+b 1 b 2 +i a 1 b 2+a 2 b 1
The answer is ' a 1 a 2 minus b 1 b 2 + i a 2 b 1+a 1 b 2 '. This is from the associative and distributive laws of real numbers extended to numbers with square root minus 1 .
z 1=a 1+i b 1 and z 2 = a 2+i b 2 . What is z 1 multiplied by z 2 ? ;; Solution : z 3 = z 1 into z 2 ;; equals a 1+i b 1 multiplied by a 2+i b 2 ;; equals a 1 into a 2+i b 2 +i b 1 into a 2+i b 2 ;; equals a1 a2+i a1 b2+i b1 a2 +i squared b1 b2 ;; equals a1 a2 minus b1 b2 + i b1 a2+a1 b2
Multiplication of two complex numbers follows numerical expression laws and properties with square root minus 1 handled as per the property square root minus 1 squared equals minus 1.
Multiplication of two complex numbers : For any complex number z1=a1+i b1 in complex numbers and z2 = a2+i b2 in complex numbers ;; z1 multiplied by z2 = a1 a2 minus b1 b2 +i a2 b1+a1 b2
Given z1=1+2i and z2=3 minus i. what is z1 multiplied by z2?
five plus five
5+5i
minus five plus
minus 5+5i
five minus
5 minus 5i
minus five minus
minus 5 minus 5i
The answer is '5+5i'

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