Conjugate of a complex number is explained.

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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 : 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
- coupled; joined ; related in reciprocal or complementary
- 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+ib in CC ` the conjugate of `z` is given as `bar(z) = a-ib`.

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

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is 'Conjugate'.

*Solved Exercise Problem: *

Find `bar(1-3i)`.

- `1-3i`
- `-1-3i`
- `1+3i`
- `1+3i`
- `-1+3i`

The answer is '`1+3i`'

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