How do i get to the correct answer 62/949 + 297/949i

Question

the problem

55.  i/(3-2i) + 2i/(3+8i)

 

my procedure:

(i(3+8i) + 2i(3-2i))/ ((3-2i)(3+8i))

 

(3i-8+6i+4)/(9+24i-6i+16)

 

(9i-4)/(25+18i)

Answer 1

Your work so far is correct.  You just need to finish by making the denominator real by multiplying top and bottom by the complex conjugate which is (25-18i)  

 

[(9i-4)/(25+18i)] * [(25-18i)/(25-18i)]  

= [225i-100+162+72i] / [625+324]  

= [62+297i]/949

= (62/949) + (297/949)i  

 

This is done to get the number in the standard a+bi form for a complex number