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Thought-Process to Discover Knowledge

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nub,

trek,

jogger,

exercise.

User Guide

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User Guide

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summary of this topic

### Algebra of Complex Numbers

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)

### Multiplication of two Complex numbers

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

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Complex numbers multiplication is explained.

Keep tapping on the content to continue learning.
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'

Progress

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