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Thought-Process to Discover Knowledge

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User Guide

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

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

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User Guide

trek is the step by step exploration of the concept.

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User Guide

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User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### Properties of Complex Number Arithmetic

Voice

Voice

Home

»  Complex Multiplication is distributive over complex addition.

→  z_1 xx (z_2 + z_3) = z_1 xx z_2 + z_1 xx z_3

### Distributive Property

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Product with sum of complex numbers is sum of, products with the complex numbers - distributive.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is distributive over complex addition.

Keep tapping on the content to continue learning.
Starting on learning "Distributive Property". ;; In this page, you will learn that the complex multiplicative is distributive over complex addition.

What does 'distribute' mean?

• to restrict; to arrest

Consider three complex numbers z_1, z_2, z_3 in CC, and the following

add first z_2+z_3 and multiply that by z_1.
multiply z_1 xx z_2 and z_1 xx z_3 and added the results.
Will they give the same result?

• Yes, the results will be the same
• No, the results will differ

The answer is "Yes, the results will be the same".

The complex numbers addition and multiplication is considered to be operations on numerical expressions of real numbers.

Given z_1 = a_1+ib_1, z_2 = a_2+ib_2, and z_3 = a_3+ib_3. What is z_1 xx (z_2 + z_3)?

• z_1 xx z_2 + z_1 xx z_3
• z_1 xx z_2 + z_3

The answer is 'z_1 xx z_2 + z_1 xx z_3'

z_1 xx (z_2 + z_3)
quad quad = z_1 xx z_2 + z_1 xx z_3

proof:
z_1 xx (z_2 + z_3)
quad quad = (a_1+ib_1) xx (a_2+a_3 + i (b_2+b_3))
quad quad = a_1a_2-b_1b_2 + i(a_1b_2+a_2b_1)
quad quad quad quad +a_1a_3-b_1b_3 + i(a_1b_3+a_3b_1)
quad quad = z_1 xx z_2 + z_1 xx z_3

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Distributive Property of Complex Numbers: For any given complex numbers z_1, z_2, z_3 in CC
z_1 xx (z_2 + z_3)
quad quad = z_1 xx z_2 + z_1 xx z_3

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given z_1z_2= 3+4i and z_2z_3=1-3i what is (z_1+z_3)z_2?

• 5i
• 4+i
• 4+7i
• -5i

The answer is '4+i'

Progress

Progress

What does 'distribute' mean?
restrict;arrest
to restrict; to arrest
Consider three complex numbers z_1, z_2, z_3 in CC , and the following

add first z_2+z_3 and multiply that by z_1 .
multiply z_1 xx z_2 and z_1 xx z_3 and added the results.
Will they give the same result?
yes;s;same
Yes, the results will be the same
no;differ
No, the results will differ
The answer is "Yes, the results will be the same".
The complex numbers addition and multiplication is considered to be operations on numerical expressions of real numbers. ;; Given z1 = a1+i b1, z2 = a2+i b2, and z3 = a3+i b3. What is z1 multiplied, z2 + z3?
1
z1 into z2 + z1 into z3
2
z1 into z2 + z3
The answer is 'z1 into z2 + z1 into z3'
z1 into, z2 + z3 ;; equals z1 into z2 + z1 into z3 ;; proof: z1 into, z2 + z3 ;; equals a1+i b1 xx, a2+a3 + i b2+b3 ;; equals a1 a2-b1 b2 + i a1 b2+a2 b1 +a1 a3-b1 b3 + i a1 b3+a3 b1 ;; equals z1 multiplied z2 + z1 multiplied z3
Product with sum of complex numbers is the sum of, products with the complex numbers- distributive.
Distributive Property of Complex Numbers: For any given complex numbers z1, z2, z3 in complex numbers ;; z1 multiplied, z2 + z3 ;; equals z1 multiplied z2, + z1 multiplied z3
Given z1 z2= 3+4i, and z2 z3=1-3i what is z1+z3, multiplied by z2?
1
2
3
4
minus 5i
The answer is ' 4+i '

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