Question

Question #0ae21

Answer 1

`(1+i)/(i(2+3i))=-1/13-5/13i`

Explanation:

Given a complex number `z=a+bi`, the complex conjugate of `z`, denoted `bar(z)`, is given by `bar(z)=a-bi`. A useful property of the complex conjugate is that `zbar(z) = a^2+b^2 in RR`. We can use this to eliminate the complex value from the denominator of the expression.

`(1+i)/(i(2+3i)) = (1+i)/(2i+3i^2)`

`=(1+i)/(-3+2i)`

`=((1+i)(-3-2i))/((-3+2i)(-3-2i))`

`=(-3-3i-2i-2i^2)/((-3)^2+2^2)`

`=(-1-5i)/13`

`=-1/13-5/13i`