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Magazine Problem 58
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=\sqrt{3}-i, \quad z_{2}=-\sqrt{3}-i$$
Problem 59
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=-2-2 \sqrt{3} i, \quad z_{2}=5 i$$
Problem 60
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=-5+5 i, \quad z_{2}=-3 i$$
Problem 62
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=2 i, \quad z_{2}=-3 i$$
Problem 63
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=4, \quad z_{2}=2-i$$
Problem 64
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=7, \quad z_{2}=3+5 i$$
Problem 64
An airplane is flying in the direction \(140^{\circ}\) with an airspeed of \(500 \mathrm{mi} / \mathrm{hr}\), and a \(30 \mathrm{mi} / \mathrm{hr}\) wind is blowing in the direction \(65^{\circ} .\) Approximate the true course and ground speed of the airplane.
Problem 65
Use trigonometric forms to find \(z_{1} z_{2}\) and \(z_{1} / z_{2}\) $$z_{1}=-5, \quad z_{2}=3-2 i$$
Problem 65
An airplane pilot wishes to maintain a true course in the direction \(250^{\circ}\) with a ground speed of \(400 \mathrm{mi} / \mathrm{hr}\) when the wind is blowing directly north at \(50 \mathrm{mi} / \mathrm{hr}\). Approximate the required airgeed and compass heading.
Problem 66
An airplane is flying in the direction \(20^{\circ}\) with an airspeed of \(300 \mathrm{mi} /\) hr. Its ground speed and true course are \(350 \mathrm{mi} / \mathrm{hr}\) and \(30^{\circ},\) respectively. Approximate the direction and speed of the wind.
