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Thought-Process to Discover Knowledge

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summary of this topic

### Algebra of Complex Numbers

Voice

Voice

Home

Complex Number Conjugate

»  Conjuage of a+ib
Conjugate means "coupled or related". Conjugate of a complex number makes the number real by addition or multiplication.

→  =bar(a+ib)
→  =a-ib

### Conjugate of a complex Number

plain and simple summary

nub

plain and simple summary

nub

dummy

Conjugate of a complex number is the number with the same real part and negative of imaginary part.

simple steps to build the foundation

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simple steps to build the foundation

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Conjugate of a complex number is explained.

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Starting on learning "Conjugate of a complex number". ;; In this page, Conjugate of a complex number is explained.

In numerical expressions or algebraic expressions, we can manipulate the expressions without modifying the value of the expression
•  add and subtract : eg 3 = 3+1-1
•  multiply and divide : eg : 3 = 3 xx 2/2
•  etc.

. These manipulations help to arrive at a different form of expressions or help to solve.

In case of complex numbers, a+ib, one modification stands out "convert the complex number to real number". This can be achieved either by addition or multiplication with the number a-ib.
•  addition (a+ib) + (a-ib) = 2a
•  multiplication (a+ib) xx (a-ib) = a^2+b^2

For a given complex number z= a+i b, the connected number that give a real number on multiplication is a-ib. It is named as conjugate of z and represented as bar(z) or bar(a+ib) = a-ib

What does 'conjugate' mean?

• coupled; joined ; related in reciprocal or complementary
• disjoint; additional; unrelated and orthogonal

The answer is 'coupled; joined ; related in reciprocal or complementary'

bar(z) is called ... of z.

• Practice Saying the Answer

The answer is 'Conjugate'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Conjugate of a Complex NumberFor a complex number z=a+ib in CC  the conjugate of z is given as bar(z) = a-ib.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Find bar(1-3i).

• 1-3i
• -1-3i
• 1+3i
• -1+3i

The answer is '1+3i'

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Progress

About you

Progress

In numerical expressions or algebraic expressions, we can manipulate the expressions without modifying the value of the expression ;; add and subtract : for example 3 = 3+1 minus 1;; multiply and divide : for example : 3 = 3 multiplied by 2 divided by 2 ;; et cetera. ;; These manipulations help to arrive at a different form of expressions or help to solve. ;; In case of complex numbers, a+i b, one modification stands out ; convert the complex number to real number. This can be achieved either by addition or multiplication with the number a minus i b. ;; addition (a+i b) + (a minus i b) = 2a ;; multiplication (a+ib) multiplied by (a minus ib) = a squared +b squared
For a given complex number z= a+i b, the connected number that give a real number on multiplication is a minus i b. It is named as conjugate of z and represented as ;; conjugate of z or; conjugate of a+i b =; a minus i b
What does 'conjugate' mean?
coupled;joined;related
coupled; joined ; related in reciprocal or complementary
disjoint;additional;unrelated
disjoint; additional; unrelated and orthogonal
The answer is 'coupled; joined ; related in reciprocal or complementary'
Conjugate of a complex number is the number with the same real part and negative of imaginary part.
Conjugate of a Complex Number: For a complex number z=a+i b in complex numbers the conjugate of z is given as conjugate of z = a minus i b.
bar of z is called?
conjugate
The answer is 'Conjugate'.
Find conjugate of 1 minus 3i
1-
1 minus 3i
minus 1 minus;-1-
minus 1 minus 3i
1+
1+3i
-1+
minus 1 plus 3i
The answer is ' 1+3i '

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