Modulus via the conjugate

#modulus#conjugate#formula

Statement

Show that $|z|=\sqrt{z\bar z}$ and compute $|3-4i|$ .

Hint

$z\bar z=a^2+b^2$ .

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Formula. $|z|=\sqrt{z\bar z}$ follows from $z\bar z=|z|^2$ .

Compute. $|3-4i|=\sqrt{9+16}=\sqrt{25}=5$ .

Conclusion. $|3-4i|=5$ .