Consider w is equal to 2 times open paren cosine of open paren 210 degrees close paren plus i sine open paren 210 degrees close paren close paren and z is equal to 2 times open paren cosine of open paren 330 degrees close paren plus i sine open paren 330 degrees close paren close paren What is w minus z expressed in rectangular form?
Answer
A
negative 2 square root of 3 minus 2 i
B
2 i
C
negative 2 i
D
negative 2 square root of 3 plus 0 i
Explanation
Using the unit-circle values, w = 2(−√3/2 − i/2) = −√3 − i, and z = 2(√3/2 − i/2) = √3 − i. Subtracting gives w − z = (−√3 − i) − (√3 − i) = −2√3 + 0i, so the rectangular form is negative 2√3 plus 0i.
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