Question

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.

Answer 1

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}`.