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

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