Plot the complex number z=9+7i and find its absolute value.

tabita57i 2021-07-19 Answered
Plot the complex number and find its absolute value.
z=9+7i

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Expert Answer

dieseisB
Answered 2021-07-20 Author has 3175 answers

Concept used:
The absolute value or modulus of complex number is the distance between the origin (0, 0) and point (a,b) in the complex plane.
Formula to find the absolute value of any complex number:
\(\displaystyle{\left|{z}\right|}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}\ {\quad\text{or}\quad}\ {\left|{z}\right|}=\sqrt{{{a}^{{{2}}}+{b}^{{{2}}}}}\).
Calculation:
The complex number is Interprets as z=a+bi can be represent as the point (a,b) in the complex plane.
The complex number z=9+7i can be represented as the point (9,7) in the complex plane.
The plot complex number z=9+7i as shown in below:

The absolute value of z=a+bi is \(\displaystyle{\left|{a}+{b}{i}\right|}=\sqrt{{{a}^{{{2}}}+{b}^{{{2}}}}}\).
\(\displaystyle{\left|{z}\right|}=\sqrt{{{9}^{{{2}}}+{7}^{{{2}}}}}\)
\(\displaystyle\Rightarrow\sqrt{{{81}+{49}}}=\sqrt{{{130}}}\).
Hence, the absolute value is \(\displaystyle\sqrt{{{130}}}\).

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