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  • Express the following expression in the form of a+ib : Q :14

Q : 14         Express the following expression in the form of  a+ib:

                        \frac{(3+i\sqrt{5})(3-i\sqrt{5})}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i\sqrt{2})}

Answers (1)

best_answer

Given problem is 
\frac{(3+i\sqrt{5})(3-i\sqrt{5})}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i\sqrt{2})}
Now, we will reduce it into 

\frac{(3+i\sqrt{5})(3-i\sqrt{5})}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i\sqrt{2})} = \frac{3^2- (\sqrt5i)^2}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i\sqrt{2})}                        (using \ (a-b)(a+b)=a^2-b^2)
                                                          =\frac{9-5i^2}{\sqrt3+\sqrt2i-\sqrt3+\sqrt2i}
                                                         =\frac{9-5(-1)}{2\sqrt2i}                                                           (\because i^2 = -1)
                                                         =\frac{14}{2\sqrt2i}\times \frac{\sqrt2i}{\sqrt2i}
                                                         =\frac{7\sqrt2i}{2i^2}
                                                         =-\frac{7\sqrt2i}{2}
Therefore, answer is 0-i\frac{7\sqrt2}{2}

Posted by

Gautam harsolia

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