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Find the positive real value of t that satisfies \(|t+2i\sqrt{3}| |6-4i| = 26 \).

 Oct 10, 2019

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 #1
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\(|t+2i\sqrt{3}||6-4i|=26\\~\\ |6-4i| = \sqrt{36+16} = \sqrt{52}=2\sqrt{13}\\~\\ |t+2i\sqrt{3}| = \dfrac{26}{2\sqrt{13}} = \sqrt{13}\\~\\ t^2 + 4\cdot 3 = 13\\ t=1\)

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 Oct 10, 2019
 #1
avatar+6196 
+1
Best Answer

\(|t+2i\sqrt{3}||6-4i|=26\\~\\ |6-4i| = \sqrt{36+16} = \sqrt{52}=2\sqrt{13}\\~\\ |t+2i\sqrt{3}| = \dfrac{26}{2\sqrt{13}} = \sqrt{13}\\~\\ t^2 + 4\cdot 3 = 13\\ t=1\)

Rom Oct 10, 2019

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