Given: \(\displaystyle{P}{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}\)

a) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},-{\frac{{{3}\pi}}{{{4}}}}+\pi\right)}\)

\(\displaystyle={\left({4},{\frac{{\pi}}{{{4}}}}\right)}\)

So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},{\frac{{\pi}}{{{4}}}}\right)}\)

Step 2

b) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}+{2}\pi\right)}\)

\(\displaystyle={\left(-{4},-{\frac{{{5}\pi}}{{{4}}}}\right)}\)

So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left(-{4},{\frac{{{5}\pi}}{{{4}}}}\right)}\)

c) \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},-{\frac{{{3}\pi}}{{{4}}}}+{3}\pi\right)}\)

\(\displaystyle={\left({4},{\frac{{{9}\pi}}{{{4}}}}\right)}\)

So, \(\displaystyle{\left(-{4},-{\frac{{{3}\pi}}{{{4}}}}\right)}={\left({4},{\frac{{{9}\pi}}{{{4}}}}\right)}\)