Question

show that root 7 + i root 3 upon root 7 minus i root 3 + root 7 minus i root 3 upon root 7 + i root 3 is real​

Answer 1

Step-by-step explanation:

Consider the provided expression.

$\frac{\sqrt{7} +i\sqrt{3}}{\sqrt{7} -i\sqrt{3}}+ \frac{\sqrt{7} -i\sqrt{3}}{\sqrt{7} +i\sqrt{3}}$

Take the LCM

$\frac{(\sqrt{7} +i\sqrt{3})^2+(\sqrt{7} -i\sqrt{3})^2}{(\sqrt{7} -i\sqrt{3})(\sqrt{7} +i\sqrt{3})}$

The value of i²=-1 and use the formula $(a+b)(a-b)=a^2-b^2$ and $(a+b)^2=a^2+b^2+2ab$

$\frac{7-3+2i\sqrt{21}+7-3-2i\sqrt{21}}{7+3}$

$\frac{14-6}{10}\\\frac{8}{10}\\\frac{4}{5}$

4/5 is a real number.

Hence proved.

Answer 2

Answer:

4/5

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