What is the rectangular form of z is equal to 40 times open paren cosine of open paren 7 pi over 6 close paren plus i sine open paren 7 pi over 6 close paren close paren ?
Answer
A
z is equal to negative 20 square root of 3 minus 20 i
B
z is equal to 20 square root of 3 minus 20 i
C
z is equal to 20 minus 20 i square root of 3
D
z is equal to negative 20 minus 20 i square root of 3
Explanation
Use the values cos(7π/6) = −√3/2 and sin(7π/6) = −1/2. Multiplying each by 40 gives z = 40(−√3/2) + 40(−1/2)i = −20√3 − 20i. Therefore, the rectangular form is choice C.
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