Modulus & Conjugate — Complex Numbers (Mathematics)

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Memorize

Modulus and Conjugate

Two operations CSCA tests constantly. Modulus is the distance from origin. Conjugate flips the sign of $i$.

∣ a + bi ∣ = a^{2} + b^{2} \overline{a + bi} = a - bi

Modulus is a distance; conjugate flips imaginary sign

$∣ z ∣$

Modulus

$a^{2} + b^{2}$ — distance from $0$

$\overset{z}{ˉ}$

Conjugate

$\overset{z}{ˉ} = a - bi$ (flip $i$ sign)

$z \overset{z}{ˉ}$

Product = $∣ z ∣^{2}$

Always real, always $\geq 0$