Kasey Haley

2022-02-02

How do you find the absolute value of $4-8i?$

Brenton Pennington

Expert

Step 1
Absolute Value or Modulus $|z|$ of a Complex No. $z=x+iy$ is defined by,
$|z|=\sqrt{{x}^{2}+{y}^{2}}$
$|4-8i|=\sqrt{{4}^{2}+\left(-8{\right)}^{2}}=\sqrt{16+64}=\sqrt{80}=4\sqrt{5}$
Taking, $\sqrt{5}\stackrel{\sim }{=}2.236$,
$|z|=4×2.236=8.944$

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