91Ó°ÊÓ

Find the product \(z_{1} z_{2}\) in standard form. Then write \(z_{1}\) and \(z_{2}\) in trigonometric form and find their product again. Finally, convert the answer that is in trigonometric form to standard form to show that the two products are equal. $$ z_{1}=-5, z_{2}=1+i \sqrt{3} $$

Find \(x\) and \(y\) so that each of the following equations is true. \((7 x-1)+4 i=2+(5 y+2) i\)

$$ \text { Graph each equation. } $$ $$ r=4+2 \cos \theta $$

Graph each complex number along with its opposite and conjugate.\(.5\)

Find the product \(z_{1} z_{2}\) in standard form. Then write \(z_{1}\) and \(z_{2}\) in trigonometric form and find their product again. Finally, convert the answer that is in trigonometric form to standard form to show that the two products are equal. $$ z_{1}=-3, z_{2}=\sqrt{3}+i $$

Find three cube roots for each of the following complex numbers. Leave your answers in trigonometric form. $$ 27\left(\cos 303^{\circ}+i \sin 303^{\circ}\right) $$

$$ \text { Graph each equation. } $$ $$ r=2+4 \cos \theta $$

We know that \(2 i \cdot 3 i=6 i^{2}=-6\). Change \(2 i\) and \(3 i\) to trigonometric form, and then show that their product in trigonometric form is still \(-6\).

Find three cube roots for each of the following complex numbers. Leave your answers in trigonometric form. $$ 4 \sqrt{3}+4 i $$

Graph each complex number along with its opposite and conjugate.\(-5-2 i\)