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Express the following numbers in the form x + iy: 2(cos 7π4+isin 7π4) - Mathematics and Statistics

Sum

Express the following numbers in the form x + iy: 

`sqrt(2)(cos  (7pi)/4 + "i" sin  (7pi)/4)`

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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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