Question

Plot the complex number and find the absolute value \sqrt{-49}

Piecewise-Defined Functions
ANSWERED
asked 2021-09-12
Plot the complex number and find the absolute value.
\(\displaystyle\sqrt{{-{49}}}\)

Expert Answers (1)

2021-09-13
Step 1
Given number
\(\displaystyle\sqrt{{-{49}}}\)
Step 2
It can be written as
\(\displaystyle\sqrt{{-{49}}}=\sqrt{{{i}^{{{2}}}{7}^{{{2}}}}}\) (Using \(\displaystyle{i}^{{{2}}}=-{1}\))
\(\displaystyle\sqrt{{{\left({7}{i}\right)}^{{{2}}}}}\)
=7i
So, a+ib=0+7i
Now the absolute value of the given number is
\(\displaystyle{\left|{a}+{i}{b}\right|}=\sqrt{{{a}^{{{2}}}+{b}^{{{2}}}}}\)
\(\displaystyle=\sqrt{{{0}^{{{2}}}+{7}^{{{2}}}}}\)
\(\displaystyle=\sqrt{{{7}^{{{2}}}}}\)
=7
Step 3
Now plot the given complex number
image
28
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...