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2013-12-16T21:48:11-02:00
z=a+bi\newline a+b=1\newline z^2=-7-24i\newline\newline (a+bi)^2=-7-24i\newline a^2+2abi+(bi)^2=a^2-b^2+2abi\newline a^2-b^2+2abi=-7-24i

Comparando os números temos:

 \left \{ {{a+b=1} \atop {a^2-b^2=-7}} \right.= \left \{ {{b=1-a} \atop {(a+b)(a-b)=-7}} \right.\newline (a+(1-a))(a-(1-a))=-7\newline 2a-1=-7\newline a=\frac{-6}{2}=-3\newline\newline b=1-a=1-(-3)=4\newline\newline z=-3+4i


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