nubtrek

Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsComplex NumbersAlgebra of Complex Numbers

Division of complex numbers

Complex numbers division is explained.



click on the content to continue..

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)`
  • `((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)`

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.

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)`

Solved Exercise Problem:

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`
  • `(10+11i)/5`

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

                            
slide-show version coming soon