Conjugates (Leaving Cert Mathematics): Flashcards

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Conjugates
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Conjugate of complex number: definition

Change the sign of the imaginary part

Notation for conjugate of zz

zˉ\bar{z}

If z=a+biz = a + bi, then zˉ=?\bar{z} = ?

a−bia - bi

zˉ\bar{z} for z=2+iz = 2 + i

2−i2 - i

zˉ\bar{z} for z=−8−2iz = -8 - 2i

−8+2i-8 + 2i

zˉ\bar{z} for z=−5iz = -5i

5i5i

zˉ\bar{z} for z=10z = 10

1010

Conjugate of a real number

The number itself

Rule for evaluating conjugate expressions

Evaluate what's under the bar first

z+w‾\overline{z+w} for z=2−3iz = 2-3i, w=2+4iw = 2+4i

4−i4 - i

z‾‾=?\overline{\overline{z}} = ?

zz

z+w‾=?\overline{z+w} = ?

z‾+w‾\overline{z} + \overline{w}

z−w‾=?\overline{z-w} = ?

z‾−w‾\overline{z} - \overline{w}

az+bw‾=?\overline{az+bw} = ? (a,ba,b real)

az‾+bw‾a\overline{z} + b\overline{w}

zw‾=?\overline{zw} = ?

z‾⋅w‾\overline{z} \cdot \overline{w}

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