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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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Complex Number Addition


 »  `(a+ib) + (c+id)`
by associative, commutative, distributive laws of real numbers and by considering `i` as a variable
    →  `=(a+c) + i(b+d)`

Addition of two Complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Addition of two complex numbers is the addition of real and imaginary parts individually.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers addition is explained.


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Starting on learning "Addition of two Complex numbers". ;; In this page, Complex numbers addition is explained.

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

  • `(a_1+a_2) + i (b_1+b_2)`
  • `a_1+ib_1`
  • `a_2+ib_2`

The answer is '`(a_1+a_2) + i (b_1+b_2)`'. This is from the associative and distributive laws of real numbers extended to numbers with `sqrt(-1)`.

Complex number Addition:
`z_1+z_2`
`quad quad =a_1+ib_1 + a_2+ib_2`
`quad quad =a_1+a_2+ib_1+ib_2` (associative law of addition)
`quad quad = a_1+a_2+ i(b_1+b_2)` (distributive law of multiplication over addition)
`quad quad =(a_1+a_2) + i (b_1+b_2)` (real and imaginary parts of result)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Addition of 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+z_2 = (a_1+a_2)+i(b_1+b_2)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given two complex numbers `3+2i` and `-1+i`, what is the sum?

  • `3+i`
  • `2+3`
  • `2+3i`
  • `2-i`

The answer is '`2+3i`'

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+z 2 ?
a1+a2
a 1+a 2 + i b 1+b 2
a1
a1 + i b 1
a2
a2+i b2
The answer is 'a 1+a 2 + i b 1+b 2'. This is from the associative and distributive laws of real numbers extended to numbers with square root minus 1
Complex number Addition: z 1+z 2 ;; equals a 1+ib 1 + a 2+i b 2 ;; equals a 1+a 2+i b 1+i b 2 ; associative law of addition ;; equals a 1+a 2+ i b 1+b 2 ; distributive law of multiplication over addition ;; equals a 1+a 2 + i b 1+b 2 ; real and imaginary parts of result
Addition of two complex numbers is the addition of real and imaginary parts individually.
Addition of Complex numbers : For any complex number z 1=a 1+i b 1 in complex numbers and z 2 = a 2+ib 2 in complex numbers;; z 1+z 2 = a 1+a 2 +i b 1+b 2
Given two complex numbers 3+2i and minus 1+i, what is the sum?
3+i
3+i
2+3
2+3
2+3i
2+3i
minus
2 minus i
The answer is ' 2+3i '

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