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Question
Express the following numbers in the form x + iy:
`sqrt(2)(cos (7pi)/4 + "i" sin (7pi)/4)`
Solution
`sqrt(2)(cos (7pi)/4 + "i" sin (7pi)/4)`
= `sqrt(2)[cos(2pi - pi/4) + "i" sin(2pi - pi/4)]`
= `sqrt(2)[cos pi/4 - "i" sin pi/4]`
= `sqrt(2)[1/sqrt(2) + "i" (-1/sqrt(2))]`
= 1 – i
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