Bilangan Polar Matematika Teknik 2

Summary

In this educational video, the presenter explains how to work with polar numbers in mathematical engineering. The process covers multiplying, dividing, and adding complex numbers in polar form, with examples using Z1 = 4 - 8i and Z2 = 7 + 6i. Key steps in the calculations are shown, such as handling imaginary numbers, using Pythagoras' theorem for finding magnitudes, and determining angles through trigonometric functions. The video also demonstrates how to visualize the results graphically, ultimately arriving at final values like Z = 11.1, angle 352.3 degrees. The presentation concludes with a polite farewell and well-wishing.

Takeaways

• 😀 The video begins with a greeting and introduction to the topic of complex numbers in polar form for a mathematics course.
• 😀 The first example involves multiplying two complex numbers, Z1 = 4 - 8i and Z2 = 7 + 6i. The calculation proceeds with distributing the terms and simplifying using i² = -1.
• 😀 After calculating the multiplication, the result of Z1 * Z2 is 76 - 32i.
• 😀 The second example involves dividing Z1 by Z2, where the denominator is multiplied by its conjugate to simplify the expression.
• 😀 In the division calculation, the result of Z1 / Z2 is approximately -20 - 80i / 85.
• 😀 For the third example, the sum of Z1 and Z2 is calculated, resulting in 11 - 2i.
• 😀 The diagram in the third example is drawn in a counterclockwise direction to represent the complex numbers on the complex plane.
• 😀 The angle for the sum of the complex numbers is found to be 270°, based on the given right-angle triangle and the sum of the angles.
• 😀 The length of the resultant vector is calculated using the Pythagorean theorem, resulting in a magnitude of approximately 11.1.
• 😀 The angle (alpha) is calculated using the arcsine function, yielding an angle of approximately 82.3°.
• 😀 Finally, the angle of the complex number is adjusted by adding the angle 270° from the third example, resulting in a total angle of 352.3°.

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