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How do you simplify #(2-sqrt2i)/(3+sqrt6i)#?

Answer 1

Cora Alexander

The answer is #=(6-sqrt12)/15-(2sqrt6+3sqrt2)/15i#

Let a complex number be #z=z_1/z_2#

To simplify, we multiply the numerator and the denominator by the conjugate of the denominator

#z=(z_1*barz_2)/(z_2*barz_2)#

If #w=a+ib#, the conjugate is #barw=a-ib#

#i^2=-1#

Here,

#z=(2-sqrt2i)/(3+sqrt6i)#

#z=((2-sqrt2i)(3-sqrt6i))/((3+sqrt6i)(3-sqrt6i))#

#=(6-2sqrt6i-3sqrt2i-sqrt12)/(9+6)#

#=(6-sqrt12)/15-(2sqrt6+3sqrt2)/15i#

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Answer 2

Elias Ackerman

To simplify ( \frac{2 - \sqrt{2}i}{3 + \sqrt{6}i} ), multiply the numerator and denominator by the conjugate of the denominator. This will eliminate the imaginary terms in the denominator. Then simplify the expression.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.