How do you find $∣ ∣ ∣ - \frac{18}{7} + \frac{\sqrt{5}}{7} i ∣ ∣ ∣$ $abs( -18/7 + sqrt5/7 i )$ ?

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How do you find $∣ ∣ ∣ - \frac{18}{7} + \frac{\sqrt{5}}{7} i ∣ ∣ ∣$ $abs( -18/7 + sqrt5/7 i )$ ?

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Answer 1 · 2016-03-26T19:44:12

$∣ ∣ ∣ - \frac{18}{7} + \frac{\sqrt{5}}{7} i ∣ ∣ ∣ = \sqrt{\frac{324}{49} + \frac{5}{49}} = \sqrt{\frac{47}{7}}$ $|-18/7+sqrt5/7i|=sqrt(324/49+5/49)=sqrt(47/7)$

Explanation:

For general complex number $z = x + i y$ $z=x+iy$ in rectangular form, the modulus is given by $| z | = \sqrt{x^{2} + y^{2}}$ $|z|=sqrt(x^2+y^2)$ .

So in this particular case we get

$∣ ∣ ∣ - \frac{18}{7} + \frac{\sqrt{5}}{7} i ∣ ∣ ∣ = \sqrt{\frac{324}{49} + \frac{5}{49}} = \sqrt{\frac{47}{7}}$ $|-18/7+sqrt5/7i|=sqrt(324/49+5/49)=sqrt(47/7)$

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How do you find $∣ ∣ ∣ - \frac{18}{7} + \frac{\sqrt{5}}{7} i ∣ ∣ ∣$ $abs( -18/7 + sqrt5/7 i )$ ?

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