What is the value of a complex conjugate for a complex number
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What is the value of a complex conjugate for a complex number

[From: ] [author: ] [Date: 12-07-01] [Hit: ]
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Enough said.

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Think of a rule you learned when studying quadratic equations: (a + b) * (a - b) = a^2 - b^2

If we used the term, a + b and a - b are conjugates.

Imagine instead a + bi. The conjugate is a - bi, so that

(a + bi)(a - bi) = a^2 + b^2

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Let the complex number = Z and the conjugate = Z َ
z = a + bi
z َ = a - bi
Only on the imaginary part (bi)
Examples :

3+5i \\\ 3-5i
i \\\ - i
7 \\\\ 7 ( there isn't imaginary part in here 7+0i = 7 - 0i )


the conjugate important rules
Z * Z َ = a^2 + b ^ 2

Z + Z َ = 2a

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given a complex number z =a +bi , its conjugate is z* = a - bi

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the complex conjugate of a+bi is a-bi
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