Question

what is (1+i)/i(2+3i) ? how do I do it?

Answer 1

1) multiply top and bottom times i.
2) use conjugate (multiply top and bottom times `2-3i`

Answer 2

\(\LARGE\color{black}{ \frac{(1+i)}{i(2+3i)} }\)

\(\LARGE\color{black}{ \frac{(1+i)\color{darkgoldenrod}{\times i} }{i(2+3i)\color{darkgoldenrod}{\times i}} }\)

\(\LARGE\color{black}{ \frac{1i-1}{-1(2+3i)} }\)

\(\LARGE\color{black}{ \frac{i-1}{-1(2+3i)} }\)

\(\LARGE\color{black}{ \frac{-(-i+1)}{-1(2+3i)} }\)

\(\LARGE\color{black}{ \frac{-(1+i)}{-1(2+3i)} }\)

\(\LARGE\color{black}{ \frac{1+i}{2+3i} }\)

Answer 3

\(\LARGE\color{black}{ \frac{(1+i)\color{red}{\times(2-3i)}}{(2+3i)\color{red}{\times(2-3i)}} }\) applying `(a+bi)(a-bi)=a²+b²` to the bottom

\(\LARGE\color{black}{ \frac{(1+i)\color{red}{\times(2-3i)}}{4+3} }\)

\(\LARGE\color{black}{ \frac{(1+i)\color{red}{\times(2-3i)}}{7} }\)

Answer 4

Then,


\(\LARGE\color{black}{ \frac{2-3i+2i+3}{7} }\)

\(\LARGE\color{black}{ \frac{5-i}{7} }\)

Answer 5

Any questions ?

Answer 6

thankyou so much! made pretty good sense to me :))