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Question
Express the following numbers in the form x + iy:
`7(cos(-(5pi)/6) + "i" sin (- (5pi)/6))`
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Solution
`cos(-(5pi)/6) = cos (5pi)/6 = cos(pi - pi/6)`
= `-cos pi/6`
= `-sqrt(3)/2`
and `sin(- (5pi)/6)`
= `-sin (5pi)/6`
= `-sin(pi - pi/6)`
= `-sin pi/6`
= `-1/2`
∴ `7[cos(-(5pi)/6) + "i" sin(-(5pi)/6)]`
= `7[ - sqrt(3)/2 + "i"(-1/2)]`
= `-(7sqrt(3))/2 - (7"i")/2`, which is of the form x + iy.
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