Question

09) O numero complexo z, tal que 5z + z = 12 + 16i, é igual a:

a) -2 + 2i b) 2 – 3i c) 1 + 2i d) 2 + 4i e) 3 + i

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Answer 1

$\large\boxed{\begin{array}{l}\sf5z+\overline{\sf z}=12+16i\\\sf 5(a+bi)+(a-bi)=12+16i\\\sf 5a+5bi+a-bi=12+16i\\\sf 6a+4bi=12+16i\\\sf 6a=12\\\sf a=\dfrac{12}{6}\\\sf a=2\\\sf 4b=16\\\sf b=\dfrac{16}{4}\\\sf b=4\\\sf z=2+4i\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}\end{array}}$