O produto entre os números complexos ( 5 + 7i) (3 - 2i) resulta em:
A) 1 + 11i
B) 1 + 31i
C) 29 + 11i
D) 29 - 11i
E) 29 + 31i
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![\mathsf{\left(5+7i\right)\cdot \left(3-2i\right)=}\\\\\mathsf{=\left(5\cdot 3\right)-\left(5\cdot 2i\right)+\left(7i\cdot 3\right)-\left(7i\cdot 2i\right)}\\\\\mathsf{=15-10i+21i-14i^2}\\\\\mathsf{=15+11i-\left[14\cdot \left(-1\right)\right]}\\\\\mathsf{=15+11i+14}\\\\\mathsf{=\:}\boxed{\mathsf{29+11i}}\: \: \checkmark](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%285%2B7i%5Cright%29%5Ccdot+%5Cleft%283-2i%5Cright%29%3D%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5Cleft%285%5Ccdot+3%5Cright%29-%5Cleft%285%5Ccdot+2i%5Cright%29%2B%5Cleft%287i%5Ccdot+3%5Cright%29-%5Cleft%287i%5Ccdot+2i%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7B%3D15-10i%2B21i-14i%5E2%7D%5C%5C%5C%5C%5Cmathsf%7B%3D15%2B11i-%5Cleft%5B14%5Ccdot+%5Cleft%28-1%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5Cmathsf%7B%3D15%2B11i%2B14%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5C%3A%7D%5Cboxed%7B%5Cmathsf%7B29%2B11i%7D%7D%5C%3A+%5C%3A+%5Ccheckmark "\mathsf{\left(5+7i\right)\cdot \left(3-2i\right)=}\\\\\mathsf{=\left(5\cdot 3\right)-\left(5\cdot 2i\right)+\left(7i\cdot 3\right)-\left(7i\cdot 2i\right)}\\\\\mathsf{=15-10i+21i-14i^2}\\\\\mathsf{=15+11i-\left[14\cdot \left(-1\right)\right]}\\\\\mathsf{=15+11i+14}\\\\\mathsf{=\:}\boxed{\mathsf{29+11i}}\: \: \checkmark")
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Gabarito: Letra C
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Gabarito: Letra C
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