SOLUTION: Find the reciprocal of each complex number. -√5 - i√2 (the "i" is the imaginary number "i") Thank You!

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Question 290041: Find the reciprocal of each complex number.
-√5 - i√2
(the "i" is the imaginary number "i")
Thank You!
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
-√5 - i√2

The reciprocal of the number above is:
1/((-sqrt(5) - i*sqrt(2))
Multiply the numberator and denominaotr by the conjugate of the denominator (that is -sqrt(5) + i*sqrt(2):
(1*(-sqrt(5) + i*sqrt(2)))/((-sqrt(5) - i*sqrt(2))*(-sqrt(5) + i*sqrt(2))) =
(-sqrt(5) + i*sqrt(2))/((-sqrt(5)*-sqrt(5) - i^2*sqrt(2)*sqrt(2)) =
(-sqrt(5) + i*sqrt(2))/(5 - (-2)) =
(-sqrt(5) + i*sqrt(2))/7