11. Graphing Complex Numbers

Given $z_1=5(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6})$ and $z_2=3(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4})$, find the product $z_1\text{・}{z}_2$.

Given $z_1=\(\frac\)23\(\left\)(\(\cos\)25\(\degree\)+i\(\sin\)25\(\degree\]\right\))$ and $z_2=\(\frac\)52\(\left\)(\(\cos\)15\(\degree\)+i\(\sin\)15\(\degree\]\right\))$, find the product $z_1・z_2$.

Given $z_1=\frac{1}{5}(\cos \frac{\pi }{2}+i\sin \frac{\pi }{2})$ and $z_2=5(\cos \frac{\pi }{5}+i\sin \frac{\pi }{5})$, find the quotient $\frac{z_1}{z_2}$.

Given $z_1=12(\cos 30°+i\sin 30°)$ and $z_2=3(\cos 50°+i\sin 50°)$, find the quotient $\frac{z_1}{z_2}$.

In Exercises 37–44, find the product of the complex numbers. Leave answers in polar form. z₁ = 6(cos 20° + i sin 20°) z₂ = 5(cos 50° + i sin 50°)

In Exercises 45–52, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form. In Exercises 49–50, express the argument as an angle between 0° and 360°.

z₁ = 20(cos 75° + i sin 75°)

z₂ = 4(cos 25° + i sin 25°)

In Exercises 45–52, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form. In Exercises 49–50, express the argument as an angle between 0° and 360°.

z₁ = cos 80° + i sin 80°

z₂ = cos 200° + i sin 200°

In Exercises 19–21, find the product of the complex numbers. Leave answers in polar form.

z₁ = 3(cos 40°+i sin 40°)

z₂ = 5(cos 70°+i sin 70°)

In Exercises 22–24, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form.

z₁ = 5 (cos 4π/3 + i sin 4π/3)

z₂ = 10 (cos π/3 + i sin π/3)

In Exercises 37–52, perform the indicated operations and write the result in standard form.

( −6 − √(−12)) / 48

In Exercises 37–52, perform the indicated operations and write the result in standard form.

√(−8) (√(−3) − √5 )

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(3√(−5) )( −4√(−12) )

In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. (2 − 3i)(1 − i) − (3 − i)(3 + i)

In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. (2 + i)² − (3 − i)²

In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. ___ ___ 5√(−16) + 3√(−81)