Write without absolute value notation: abs(6-5i)

Question
Piecewise-Defined Functions
asked 2021-02-13
Write without absolute value notation: \(\displaystyle{\left|{{6}-{5}{i}}\right|}\)

Answers (1)

2021-02-14
Step 1
Absolute value of a complex number:
The absolute value of a complex number z=x+iy is given by \(\displaystyle{\left|{{z}}\right|}={\left|{{x}+{i}{y}}\right|}=\sqrt{{{x}^{{2}}+{y}^{{2}}}}\).
The given complex number is 6-5i.
Step 2
Evaluate the value of \(\displaystyle{\left|{{6}−{5}{i}}\right|}\) as follows.
\(\displaystyle{\left|{{6}-{5}{i}}\right|}=\sqrt{{{6}^{{2}}+{\left(-{5}\right)}^{{2}}}}\)
\(\displaystyle=\sqrt{{{36}+{25}}}\)
\(\displaystyle=\sqrt{{{61}}}\)
\(\displaystyle\approx{7.81}\)
Therefore, the absolute value of \(\displaystyle{\left|{{6}−{5}{i}}\right|}\) is 7.81.
0

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