Question

Resolva em $\mathbb{C}$ (conjunto dos números complexos) cada uma das equações:
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a) x² - 2x + 2 = 0

b) 2x² + 98 = 0
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Answer 1

$a)\\\\x^2-2x+2=0\\\\a=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ b=-2\ \ \ \ \ \ \ \ \ \ \ \ \ c=2\\\\\Delta=b^2-4ac\\\Delta=(-2)^2-4\cdot{(1)}\cdot{2}\\\Delta=4-8\\\Delta=-4$

$x= \dfrac{-b \frac{+}{-} \sqrt{\Delta}}{2a}\\\\\\\Delta= \dfrac{-(-2) \frac{+}{-} \sqrt{-4}}{2}\\\\\\{i}^2=-1\\\\x= \dfrac{2 \frac{+}{-} \sqrt{4\cdot{i}^2}}{2}\\\\\\x=\dfrac{2 \frac{+}{-}2i }{2}\\\\\\x'=\dfrac{2+2i}{2}\\\\\\x'=\dfrac{2}{2}+ \dfrac{2}{2}i\\\\\\\boxed{x'=1+i}\\\\\\x"=\dfrac{2-2i}{2}\\\\\\x"=\dfrac{2}{2}-\dfrac{2}{2}i\\\\\\\boxed{x"=1-i}$

$b)\\\\2x^2+98=0\\2x^2=-98\\\\x^2= \dfrac{-98}{2}\\\\\\x^2=-49\\\\x= \sqrt{-49}\\\\{i}^2=-1\\\\x= \sqrt{49\cdot{i}^2}\\\\x'=7i\\\\x"=-7i$