What is the product of 16 times open paren cosine of open paren 47 degrees close paren plus i sine open paren 47 degrees close paren close paren and 4 times open paren cosine of open paren 12 degrees close paren plus i sine open paren 12 degrees close paren close paren ?

To multiply complex numbers in trigonometric form, multiply their magnitudes and add their angles. The magnitudes give 16 × 4 = 64, and the angles give 47° + 12° = 59°. So the product is 64(cos 59° + i sin 59°), which is choice D.

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