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Magazine Problem 61
Write \(z_{1}\) and \(z_{2}\) in polar form, and then find the product \(z_{1} z_{2}\) and the quotients \(z_{1} / z_{2}\) and \(1 / z_{1}\). $$z_{1}=\sqrt{3}+i, \quad z_{2}=1+\sqrt{3} i$$
Problem 61
Convert the polar equation to rectangular coordinates. $$r=\frac{1}{\sin \theta-\cos \theta}$$
Problem 62
Compare the polar equation of the circle \(r=2\) with its equation in rectangular coordinates. In which coordinate system is the equation simpler? Do the same for the equation of the fourleaved rose \(r=\sin 2 \theta .\) Which coordinate system would you choose to study these curves?
Problem 62
Write \(z_{1}\) and \(z_{2}\) in polar form, and then find the product \(z_{1} z_{2}\) and the quotients \(z_{1} / z_{2}\) and \(1 / z_{1}\). $$z_{1}=\sqrt{2}-\sqrt{2} i, \quad z_{2}=1-i$$
Problem 62
Convert the polar equation to rectangular coordinates. $$r=\frac{1}{1+\sin \theta}$$
Problem 63
Convert the polar equation to rectangular coordinates. $$r=\frac{4}{1+2 \sin \theta}$$
Problem 63
Compare the rectangular equation of the line \(y=2\) with its polar equation. In which coordinate system is the equation simpler? Which coordinate system would you choose to study lines?
Problem 63
Write \(z_{1}\) and \(z_{2}\) in polar form, and then find the product \(z_{1} z_{2}\) and the quotients \(z_{1} / z_{2}\) and \(1 / z_{1}\). $$z_{1}=2 \sqrt{3}-2 i, \quad z_{2}=-1+i$$
Problem 64
Write \(z_{1}\) and \(z_{2}\) in polar form, and then find the product \(z_{1} z_{2}\) and the quotients \(z_{1} / z_{2}\) and \(1 / z_{1}\). $$z_{1}=-\sqrt{2} i, \quad z_{2}=-3-3 \sqrt{3} i$$
Problem 64
Convert the polar equation to rectangular coordinates. $$r=\frac{2}{1-\cos \theta}$$
