Determine the absolute value of each of the following complex numbers:a. z = 5 + 12i b. 2 - 3i.

necessaryh 2021-03-11 Answered

Determine the absolute value of each of the following complex numbers:
a. \(z = 5 + 12i\)
b. \(2 - 3i.\)

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Expert Answer

Usamah Prosser
Answered 2021-03-12 Author has 7689 answers

a. The absolute value of a complex number is its distance from the origin. If \(z=a+ bi\), then \(\displaystyle{\left|{z}\right|}={\left|{a}+{b}{i}\right|}=\sqrt{{{a}^{{2}}+{b}^{{2}}}}\)
The absolute value of a complex number \(z=5+12i\) is,
\(\displaystyle{\left|{z}\right|}={\left|{5}+{12}{i}\right|}=\sqrt{{{5}^{{2}}+{12}^{{2}}}}=\sqrt{{{25}+{144}}}=\sqrt{{169}}=\sqrt{{13}}\)
b. The absolute value of a complex number \(z=2−3i\) is,
\(\displaystyle{\left|{Z}\right|}={\left|{2}-{3}{i}\right|}=\sqrt{{{2}^{{2}}+{\left(-{3}\right)}^{{2}}}}=\sqrt{{{4}+{9}}}=\sqrt{{13}}\)

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