Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Test 1 => Topic started by: Milan Miladinovic on October 14, 2020, 03:42:15 PM

I'm having trouble understanding where the $1+i$ term comes from in the following line:
$\dfrac{e^{3z}  e^{3z}}{e^{3z} + e^{3z}} = 1 + 2i \implies e^{6z} = 1 + i$.
I've tried the following:
$$\begin{align*}
\dfrac{e^{3z}  e^{3z}}{e^{3z} + e^{3z}} &= 1 + 2i\\
\dfrac{e^{6z}  1}{e^{6z} + 1} &= 1 + 2i\\
e^{6z}  1 &= (1 + 2i)(e^{6z} + 1)\\
e^{6z} &= (1 + 2i)(e^{6z} + 1) + 1
\end{align*}$$
How do we get from $(1 + 2i)(e^{6z} + 1) + 1$ to $1 + i$? Have I done something wrong somewhere in my calculation?

This is how I got the answer, hope this helps!

Awesome, that makes sense! I was overthinking it