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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

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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`

*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*

trek

*simple steps to build the foundation*

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Conjugate of a complex number is explained.

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 Number**For 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`'

*your progress details*

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 '