Question

(6+6i)/(7+6i)

Answer 1

\[\frac{ 6+6i }{ 7+6i }\]
multiply it by the conjugate of the denominator.....which is 7-6i
\[\frac{ 6+6i }{ 7+6i } \times \frac{ 7-6i }{ 7-6i }\]
\[\frac{ (6+6i)(7-6i) }{ (7+6i)(7-6i) }\]
using the fact that \[(a+b)(a-b)=a^2-b^2\] i am going to expand the denominator using that..
\[\frac{ 42 -36i +42i -36i^2 }{ (7)^2-(6i)^2 }\]

Answer 2

knowing that \[i^2=-1,\]
\[\frac{ 78 +6i }{ 49-(-36) }\]
\[\frac{ 78+6i }{ 85 }\]
\[\frac{ 78 }{ 85 }+\frac{ 6 }{ 85 }i\]

Answer 3

sorry, if i have made any arithmetic mistake...