MAT334--2020F > Test 1

2020S-TT1 Q1

(1/1)

**Milan Miladinovic**:

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?

**Maria-Clara Eberlein**:

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

**Milan Miladinovic**:

Awesome, that makes sense! I was overthinking it

Navigation

[0] Message Index

Go to full version