Question

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

Piecewise-Defined Functions
Plot the complex number and find the absolute value.
$$\displaystyle\sqrt{{-{49}}}$$

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