Divide. Leave your answer in trigonometric form. 10(cos(57°) + i sin(57°))4(cos(39°) + i sin(39°))
Question
Divide. Leave your answer in trigonometric form. 10(cos(57°) + i sin(57°))4(cos(39°) + i sin(39°))
Solution
To divide two complex numbers in trigonometric form, you divide the magnitudes and subtract the angles.
The magnitude of the first complex number is 10 and its angle is 57°. The magnitude of the second complex number is 4 and its angle is 39°.
Step 1: Divide the magnitudes 10 ÷ 4 = 2.5
Step 2: Subtract the angles 57° - 39° = 18°
So, the result of the division is 2.5(cos(18°) + i sin(18°)).
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