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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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Complex Number Subtraction


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

Subtraction of Complex Numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Subtraction of two complex numbers is the subtraction 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 subtraction is explained


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Starting on learning "Subtraction of Complex Numbers". ;; In this page, Complex numbers subtraction 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 Subtraction:
`z_1-z_2`
`quad quad =a_1+ib_1 - (a_2+ib2)`
`quad quad =a_1-a_2+ib_1-i_b2` (associative law)
`quad quad = a_1-a_2+ i(b_1-b2)` (distributive law)
`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

Subtraction 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 `z_1 = 2.1+i` and `z_2 = -2.1+i` What is `z_1-z_2`?

  • `4.2+2i`
  • `4.2`
  • `4.2-2i`
  • `-4.2+2i`

The answer is '`4.2`'

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Progress

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Progress

Consider two complex numbers z1=a1+i b1 and z2 = a2+i b2. What is z1 minus z2?
a1 minus a2
a1 minus a2 + i b1 minus b2
a1
a1 minus i b1
a2
a2 minus i b2
The answer is 'a1 minus a2 + i b1 minus b2'. This is from the associative and distributive laws of real numbers extended to numbers with square root minus 1.
Complex number Subtraction: z1 minus z2 ;; equals a1+i b1 minus a2+i b2 ;; equals a1 minus a2+i b1 minus i b2 ; associative law ;; equals a1 minus a2+ i b1 minus b2 ; distributive law ;; equals a1 minus a2 + i b1 minus b2 ; real and imaginary parts of result
Subtraction of two complex numbers is the subtraction of real and imaginary parts individually.
Subtraction of Complex numbers : For any complex number z1=a1+i b1 in complex numbers and z2 = a2+i b2 in complex numbers ;; z1 minus z2 = a1 minus a2+i b1 minus b2
Given z 1 = 2 point 1+i and z 2 = minus 2 point 1+i. What is z 1 minus z 2 ?
plus 2i;
4 point 2+2i
4.2
4 point 2
minus 2i
4 point 2 minus 2i
minus 4.2
minus 4 point 2+2i
The answer is ' 4 point 2 '

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