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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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Complex Number Division


 »  `(a+ib) -: (c+id)`
by multiplicative identity, multiplicative inverse, distributive properties.

    →  `= (a+ib)/(c+id) ``xx (c-id)/(c-id)`

    →  `= ((a+ib)xx(c-id)) / (c^2+d^2)`

Division of complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Division of two complex numbers follows numerical expression laws and properties with `i` handled as `(sqrt(-1))^2 = -1` to arrive at `a+bi` form.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers division is explained.


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Starting on learning "Division of Complex Numbers". ;; In this page, Complex numbers division 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` in `a+bi` form?

  • `(a_1a_2+b_1b_2) + i (a_2b_1-a_1b_2)`
  • `a_1/a_2+ib_1/b_2`
  • `((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)`

The answer is '`((a_1a_2+b_1xxb_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)`'

`z_1=a_1+ib_1` and `z_2 = a_2+ib_2`. What is `z_1 / z_2`?
Solution :
`z_3 = z_1 / z_2 `
`quad quad = (a_1+ib_1)/(a_2+ib_2)`
`quad quad = (a_1+ib_1)/(a_2+ib_2) xx (a_2-ib_2)/(a_2-ib_2) `
`quad quad = ((a_1+ib_1)xx (a_2-ib_2))/((a_2+ib_2) xx (a_2-ib_2)) `
`quad quad = ((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Division 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 / z_2 =` `((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `z_1 = 10+5i` and `z_2=3-4i` what is `z_1/z_2`?

  • `(6+8i)/5`
  • `(3i+4)/25`
  • `10+11i`
  • `(10+11i)/5`

The answer is '`(10+11i)/5`'.

your progress details

Progress

About you

Progress

Consider two complex numbers z1=a1+i b1 and z2 = a2+i b2. What is z1 / z2 in a+b i form?
1
a1 a2+b1 b2 + i a2 b1 minus a1 b2
2
a1 by a2+i b1 by b2
3
a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
The answer is a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
z1=a1+i b1 and z2 = a2+i b2. What is z1 / z2? ;; Solution : ;; z3 = z1 by z2 ;; equals a1+i b1 by a2+i b2 ;; equals a1+i b1 by a2+i b2 multiplied by a2 minus i b2 by a2 minus i b2 ;; equals a1+i b1 multiplied by a2 minus i b2 divided by a2+i b2 multiplied by a2 minus i b2 ;; equals a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
Division of two complex numbers follows numerical expression laws and properties with i handled as square root of minus 1 whole squared = minus 1, to arrive at a+b i form.
Division of two complex numbers : For any complex number z1=a1+i b1 in complex numbers and z2 = a2+i b2 in complex numbers ;; z1 divided by z2 = a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared + b2 squared
Given z1 = 10+5i and z2=3 minus 4i. what is z1 by z2?
6;8
6_8i by 5
3;3i;
3i+4 by 25
10;11
10+11i
11i by 5
10+11i by 5
The answer is '10+11i by5'.

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