Express the following in the form a+ib:frac{5 | vedclass

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(B) To express the complex number in the form $a+ib$,we multiply the numerator and the denominator by the conjugate of the denominator:$\frac{5+\sqrt{

Vedclass · Accepted Answer

$1+2\sqrt{2}i$

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(B) To express the complex number in the form $a+ib$,we multiply the numerator and the denominator by the conjugate of the denominator:$\frac{5+\sqrt{2}i}{1-\sqrt{2}i} = \frac{5+\sqrt{2}i}{1-\sqrt{2}i} 	imes \frac{1+\sqrt{2}i}{1+\sqrt{2}i}$$= \frac{5(1) + 5(\sqrt{2}i) + (\sqrt{2}i)(1) + (\sqrt{2}i)(\sqrt{2}i)}{1^2 - (\sqrt{2}i)^2}$$= \frac{5 + 5\sqrt{2}i + \sqrt{2}i + 2i^2}{1 - 2i^2}$Since $i^2 = -1$,we have:$= \frac{5 + 6\sqrt{2}i - 2}{1 - 2(-1)} = \frac{3 + 6\sqrt{2}i}{1 + 2}$$= \frac{3 + 6\sqrt{2}i}{3} = 1 + 2\sqrt{2}i$

Express the following in the form $a+ib$:
$\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$

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Express the following in the form $a+ib$:$\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$