How do you simplify 2(cos⁡(3π4)+isin⁡(3π4))⋅2(cos⁡(π2)+isin⁡(π2)) and express the result in rectangular form?

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Micheal Hensley · Accepted Answer

2(cos⁡(3π4)+isin⁡(3π4))⋅2(cos⁡(π2)+isin⁡(π2)) =22{cos⁡(3π4)cos⁡(π2)+icos⁡(3π4)sin⁡(π2)+icos⁡(π2)sin⁡(3π4)+i2sin⁡(3π4)sin⁡(3π4)sin⁡(π2)} =22{cos⁡(3π4)cos⁡(π2)−sin⁡(3π4)sin⁡(π2)+i(cos⁡(3π4)sin⁡(π2)+icos⁡(π2)sin⁡(3π4))} =22{cos⁡(3π4+π2)+isin⁡(3π4+π2)} =22(cos⁡(5π4)+isin⁡(5π4)) 22(−cos⁡(π4)−isin⁡(π4)) =22(−12−i12) =−2−2i

How do you simplify 2(cos⁡(3π4)+isin⁡(3π4))⋅2(cos⁡(π2)+isin⁡(π2)) and express the result in rectangular form?

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