Server Not Reachable. *This may be due to your internet connection or the nubtrek server is offline.*

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

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

Voice

Voice

Home

Complex number multiplication

» `(a+ib) xx (c+id)`*by associative, commutative, distributive laws of real numbers, considering `i` as a variable, and applying `i^2=-1`*

→ `=(ac-bd) + i(cb+ad)`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Multiplication of two complex numbers follows numerical expression laws and properties with `sqrt(-1)` handled as per the property `(sqrt(-1))^2 = -1`

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

*To stop this message from appearing, please choose an option and make a payment.*

Complex numbers multiplication is explained.

Starting on learning "Multiplication of two complex numbers". ;; In this page, complex numbers multiplication is explained.

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

- `(a_1a_2-b_1b_2) + i (a_2b_1+a_1b_2)`
- `a_1a_2+ib_1b_2`
- `(a_1a_2+b_1b_2)+i(a_1b_2+a_2b_1)`

The answer is '`(a_1a_2-b_1b_2) + i (a_2b_1+a_1b_2)`'. This is from the associative and distributive laws of real numbers extended to numbers with `sqrt(-1)`.

`z_1=a_1+ib_1` and `z_2 = a_2+ib_2`. What is `z_1 xx z_2`?

Solution :

`z_3 = z_1 xx z_2 `

`quad quad = (a_1+ib_1)xx(a_2+ib_2)`

`quad quad = a_1 xx(a_2+ib_2)`

`quad quad quad quad +i b_1xx (a_2+ib_2) `

`quad quad = a_1a_2+ia_1b_2+ib_1a_2`

`quad quad quad quad +i^2b_1b_2`

`quad quad = (a_1a_2-b_1b_2) `

`quad quad quad quad + i(b_1a_2+a_1b_2)`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** Multiplication 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 xx z_2 = (a_1a_2-b_1b_2)`

`quad quad quad quad quad +i(a_2b_1+a_1b_2)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given `z_1=1+2i` and `z_2=3-i` what is `z_1 xx z_2`?

- `5+5i`
- `-5+5i`
- `5-5i`
- `-5-5i`

The answer is '`5+5i`'

*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 multiplied by z 2 ?

option 1

a 1 a 2 minus b 1 b 2 + i a 2 b 1+a 1 b 2

option 2

a 1 a 2+i b 1 b 2

option 3

a 1 a 2+b 1 b 2 +i a 1 b 2+a 2 b 1

The answer is ' a 1 a 2 minus b 1 b 2 + i a 2 b 1+a 1 b 2 '. This is from the associative and distributive laws of real numbers extended to numbers with square root minus 1 .

z 1=a 1+i b 1 and z 2 = a 2+i b 2 . What is z 1 multiplied by z 2 ? ;; Solution : z 3 = z 1 into z 2 ;; equals a 1+i b 1 multiplied by a 2+i b 2 ;; equals a 1 into a 2+i b 2 +i b 1 into a 2+i b 2 ;; equals a1 a2+i a1 b2+i b1 a2 +i squared b1 b2 ;; equals a1 a2 minus b1 b2 + i b1 a2+a1 b2

Multiplication of two complex numbers follows numerical expression laws and properties with square root minus 1 handled as per the property square root minus 1 squared equals minus 1.

Multiplication of two complex numbers : For any complex number z1=a1+i b1 in complex numbers and z2 = a2+i b2 in complex numbers ;; z1 multiplied by z2 = a1 a2 minus b1 b2 +i a2 b1+a1 b2

Given z1=1+2i and z2=3 minus i. what is z1 multiplied by z2?

five plus five

5+5i

minus five plus

minus 5+5i

five minus

5 minus 5i

minus five minus

minus 5 minus 5i

The answer is '5+5i'