SOLUTION: Please help and show all work. Divide: (1+5i)/(6−7i).Write your answer in a+bi form .Divide: (−3−2i)/(4+2i). Write your answer in a+bi form.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please help and show all work. Divide: (1+5i)/(6−7i).Write your answer in a+bi form .Divide: (−3−2i)/(4+2i). Write your answer in a+bi form.       Log On


   

Question 1015382: Please help and show all work.

Divide: (1+5i)/(6−7i).Write your answer in a+bi form


.Divide: (−3−2i)/(4+2i). Write your answer in a+bi form.





Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing yours for you.  I'll do two others ones
exactly step-by-step like your two.  Follow the EXACT
same steps.

%282%2B7i%29%2F%288-9i%29

Form the conjugate of the denominator, which is
like 8-9i except change the sign of the coefficient of i.
The conjugate of 8-9i is 8+9i

Put that conjugate over itself to form a fraction which
equals 1:  That fraction is %288%2B9i%29%2F%288%2B9i%29.
Multiply the given fraction by that:



FOIL out the top and bottom:

%2816%2B18i%2B56i%2B63i%5E2%29%2F%2864%2B72i-72i-81i%5E2%29



Combine like terms

%2816%2B74i%2B63i%5E2%29%2F%2864-81i%5E2%29

Substitute (-1) for the i2's

%2816%2B74i%2B63%28-1%29%5E%22%22%29%2F%2864-81%28-1%29%5E%22%22%29

%2816%2B74i-63%5E%22%22%29%2F%2864%2B81%5E%22%22%29

Combine like terms:

%28-47%2B74i%29%2F%28145%29

Break into two fractions:

-47%2F145%2B74i%2F145

Put the i after the fraction:

-47%2F145%2Bexpr%2874%2F145%29i

--------------------------------

%282-9i%29%2F%286%2B8i%29

Form the conjugate of the denominator, which is
like 6+8i except change the sign of the coefficient of i.
The conjugate of 6+8i is 6-8i

Put that conjugate over itself to form a fraction which
equals 1:  That fraction is %286-8i%29%2F%286-8i%29.
Multiply the given fraction by that:



FOIL out the top and bottom:

%2812-16i-54i-72i%5E2%29%2F%2836-48i%2B48i-64i%5E2%29

Combine like terms

%2812-70i%2B72i%5E2%29%2F%2836-64i%5E2%29

Substitute (-1) for the i2's

%2812-70i%2B72%28-1%29%5E%22%22%29%2F%2836-64%28-1%29%5E%22%22%29

%2812-70i-72%5E%22%22%29%2F%2836%2B64%5E%22%22%29

Combine like terms:

%28-60-70i%29%2F%28100%29

Break into two fractions:

expr%28%28-60%29%2F%28100%29%29-%2870i%29%2F%28100%29

Reduce the fractions

-3%2F5-%287i%29%2F10


Put the i after the fraction:

-3%2F5-expr%287%2F10%29i

Now do yours exactly step-by step like these two.

Edwin