Modulus (Leaving Cert Mathematics): Flashcards

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Modulus
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Modulus of a real number

Magnitude or distance to origin 00

Modulus of complex number

Distance to origin 0+0i0+0i

Modulus formula for z=a+biz=a+bi

∣z∣=a2+b2|z|=\sqrt{a^2+b^2}

∣z∣|z| for z=2+3iz=2+3i

13\sqrt{13} or approx 3.613.61

Property: ∣az∣|az| where aa is real constant

∣a∣⋅∣z∣|a| \cdot |z|

Property: ∣zw∣|zw|

∣z∣⋅∣w∣|z| \cdot |w|

Property: ∣z‾∣|\overline{z}|

∣z∣|z|

Geometric effect of conjugate on complex number

Flips symmetrically over real axis

Distance to origin for conjugate vs original

Remains the same

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