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Thought-Process to Discover Knowledge

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

nub,

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jogger,

exercise.

User Guide

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User Guide

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User Guide

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User Guide

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summary of this topic

### Algebra of Complex Numbers

Voice

Voice

Home

»  (a+ib) + (c+id)
by associative, commutative, distributive laws of real numbers and by considering i as a variable
→  =(a+c) + i(b+d)

### Addition of two Complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Addition of two complex numbers is the addition of real and imaginary parts individually.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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

• (a_1+a_2) + i (b_1+b_2)
• a_1+ib_1
• a_2+ib_2

The answer is '(a_1+a_2) + i (b_1+b_2)'. This is from the associative and distributive laws of real numbers extended to numbers with sqrt(-1).

z_1+z_2
quad quad =a_1+ib_1 + a_2+ib_2
quad quad =a_1+a_2+ib_1+ib_2 (associative law of addition)
quad quad = a_1+a_2+ i(b_1+b_2) (distributive law of multiplication over addition)
quad quad =(a_1+a_2) + i (b_1+b_2) (real and imaginary parts of result)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Addition of 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_1+a_2)+i(b_1+b_2)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given two complex numbers 3+2i and -1+i, what is the sum?

• 3+i
• 2+3
• 2+3i
• 2-i

The answer is '2+3i'

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+z 2 ?
a1+a2
a 1+a 2 + i b 1+b 2
a1
a1 + i b 1
a2
a2+i b2
The answer is 'a 1+a 2 + i b 1+b 2'. This is from the associative and distributive laws of real numbers extended to numbers with square root minus 1
Complex number Addition: z 1+z 2 ;; equals a 1+ib 1 + a 2+i b 2 ;; equals a 1+a 2+i b 1+i b 2 ; associative law of addition ;; equals a 1+a 2+ i b 1+b 2 ; distributive law of multiplication over addition ;; equals a 1+a 2 + i b 1+b 2 ; real and imaginary parts of result
Addition of two complex numbers is the addition of real and imaginary parts individually.
Addition of Complex numbers : For any complex number z 1=a 1+i b 1 in complex numbers and z 2 = a 2+ib 2 in complex numbers;; z 1+z 2 = a 1+a 2 +i b 1+b 2
Given two complex numbers 3+2i and minus 1+i, what is the sum?
3+i
3+i
2+3
2+3
2+3i
2+3i
minus
2 minus i
The answer is ' 2+3i '

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