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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

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

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

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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)`

*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.

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'.