Thread: Other opinion needed

(-4-39i)/(5-2i)

Hello Forum I worked this problem out and I just wanted to know is this seems right..

(-4-39i)/(5-2i)

Rationalize the denominator with the complex conjugate to remove the imaginary term from the denominator.
(-4-39i)/(5-2i)*(5+2i)/(5+2i)

Multiply out the complex conjugate factors in the denominator to remove the imaginary terms.
((-4-39i)(5+2i))/(29)

Simplify the expression.
(58-203i)/(29)

Factor out the GCF of 29 from each term in the polynomial.
(29(2)+29(-7i))/(29)

Factor out the GCF of 29 from 58-203i.
(29(2-7i))/(29)

Reduce the expression (29(2-7i))/(29) by removing a factor of 29 from the numerator and denominator.
(2-7i)

Remove the parentheses around the expression 2-7i.
2-7i

Originally Posted by AlgebraicallyChallenged

(-4-39i)/(5-2i)

Hello Forum I worked this problem out and I just wanted to know is this seems right..

(-4-39i)/(5-2i)

Rationalize the denominator with the complex conjugate to remove the imaginary term from the denominator.
(-4-39i)/(5-2i)*(5+2i)/(5+2i)

Multiply out the complex conjugate factors in the denominator to remove the imaginary terms.
((-4-39i)(5+2i))/(29)

Simplify the expression.
(58-203i)/(29)

Factor out the GCF of 29 from each term in the polynomial.
(29(2)+29(-7i))/(29)

Factor out the GCF of 29 from 58-203i.
(29(2-7i))/(29)

Reduce the expression (29(2-7i))/(29) by removing a factor of 29 from the numerator and denominator.
(2-7i)

Remove the parentheses around the expression 2-7i.
2-7i

Correct.