How do you find $| - 5 i |$ $abs(-5i)$ ?

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How do you find $| - 5 i |$ $abs(-5i)$ ?

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Answer 1 · 2016-06-06T00:36:24

Apply the definition $| a + b i | = \sqrt{a^{2} + b^{2}}$ $|a+bi| = sqrt(a^2+b^2)$ to find that

$| - 5 i | = 5$ $|-5i| = 5$

Explanation:

The modulus of a complex number $a + b i$ $a+bi$ , denoted $| a + b i |$ $|a+bi|$ , is given by

$| a + b i | = \sqrt{a^{2} + b^{2}}$ $|a+bi| = sqrt(a^2+b^2)$ .

and is an extension of the absolute value function, which applies to reals. The latter represents the distance from the real number to $0$ $0$ on the number line, and the former represents the distance of the complex number to the origin on the complex plane.

Applying this definition to our given complex number, we have:

$| - 5 i | = | 0 + (- 5) i |$ $|-5i| = |0+(-5)i|$

$= \sqrt{0^{2} + {(- 5)}^{2}}$ $=sqrt(0^2+(-5)^2)$

$= \sqrt{0 + 25}$ $=sqrt(0+25)$

$= \sqrt{25}$ $=sqrt(25)$

$= 5$ $=5$

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How do you find $| - 5 i |$ $abs(-5i)$ ?

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How do you find |−5i|abs(-5i)?

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How do you find $| - 5 i |$ $abs(-5i)$ ?