How would I perform the operation 14(cos 63° + isin 63°)/20(cos 15° + isin 15°)? Make sure to leave the result in trigonometric form.

1 Answer
Bill K.
Oct 9, 2015

The quick way to do it is to divide the moduli ("lengths") and subtract the arguments ("angles"). The answer is 7/10 (cos(48^{circ})+i sin(48^{circ}))

Explanation:

Note that 14(cos(63^{circ})+isin(63^{circ})) has modulus 14 and argument 63^{circ} while 20(cos(15^{circ})+i sin(15^{circ})) has modulus 20 and argument 15^{circ}.

The answer follows since 14/20=7/10 and 63^{circ}-15^{circ}=48^{circ}.

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