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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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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.

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trek

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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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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