SOLUTION: express in the form a+bi: 1+2i/ 1- square root of -64

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: express in the form a+bi: 1+2i/ 1- square root of -64      Log On


   

Question 993057: express in the form a+bi:

1+2i/ 1- square root of -64
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1+2i/ 1- square root of -64
%281%2B2i%29%2F%281-sqrt%28-64%29%29

Change sqrt%28-64%29 to sqrt%28-1%2A64%29 to sqrt%28-1%29%2Asqrt%2864%29 to i%2A8 to 8i

%281%2B2i%29%2F%281-8i%29

Multiply by the conjugate of the denominator over itself %281%2B8i%29%2F%281%2B8i%29
which we can do because that is just multiplying by 1.

%28%281%2B2i%29%281%2B8i%29%29%2F%28%281-8i%29%281%2B8i%29%29

Use FOIL on top and bottom:

%281%2B8i%2B2i%2B16i%5E2%29%2F%281%2B8i-8i-64i%5E2%29

Combine like terms and eliminate terms that have 0 sum:

%281%2B10i%2B16i%5E2%29%2F%281-64i%5E2%29

Substitute -1 for i2

%281%2B10i%2B16%28-1%29%29%2F%281-64%28-1%29%29

%281%2B10i-16%29%2F%281%2B64%29

Combine like terms:

%28-15%2B10i%29%2F65

To express in terms of a+bi, break into two fractions:

-15%2F65%2B10i%2F65

Reduce the fractions:

-3%2F13%2B2i%2F13

Move the i factor in the second term from the numerator
to the right:

-3%2F13%2Bexpr%282%2F13%29i 

Edwin