Question

Determine the absolute value of the complex number 2 - 3i.

Piecewise-Defined Functions
ANSWERED
asked 2020-11-10
Determine the absolute value of the complex number \(\displaystyle{2}-{3}{i}\).

Answers (1)

2020-11-11
Step 1
Absolute value of complex number \(\displaystyle{z}={a}+{i}{b}\) is represent by \(\displaystyle{\left|{z}\right|}\) and given as
\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left({a}\right)}^{{{2}}}+{\left({b}\right)}^{{{2}}}}}\)
Step 2
Given complex number is
\(\displaystyle{z}={2}−{3}{i}\)
Step 3
\(\displaystyle{z}={2}+{\left(−{3}\right)}{i}\)
Here
\(\displaystyle{x}={2}{y}=−{3}\)
Now
\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left({2}\right)}^{{{2}}}+{\left(-{3}\right)}^{{{2}}}}}\)
\(\displaystyle=\sqrt{{{4}+{9}}}\)
\(\displaystyle=\sqrt{{{13}}}\)
Step 4
Answer:
Absolute value of complex number \(\displaystyle{2}−{3}{i}\) is \(\displaystyle\sqrt{{{13}}}\).
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