I am doing some matrix multiplication, and at one point it is stated that,

$$\left(\begin{array}{cc}1& 0\\ 0& {e}^{\frac{i\pi}{4}}\end{array}\right)\left(\begin{array}{c}1\\ i\end{array}\right)\text{}=\left(\begin{array}{c}1\\ {e}^{i\frac{3\pi}{4}}\end{array}\right)$$

but how does $i{e}^{i\frac{\pi}{4}}={e}^{i\frac{3\pi}{4}}$?

I have tried taking Euler's formula but I can only get it to reduce down

$$\frac{-i-1}{\sqrt{2}i}$$

I have also tried converting to polar form, but I just really can't see how these two are equivalent.

$$\left(\begin{array}{cc}1& 0\\ 0& {e}^{\frac{i\pi}{4}}\end{array}\right)\left(\begin{array}{c}1\\ i\end{array}\right)\text{}=\left(\begin{array}{c}1\\ {e}^{i\frac{3\pi}{4}}\end{array}\right)$$

but how does $i{e}^{i\frac{\pi}{4}}={e}^{i\frac{3\pi}{4}}$?

I have tried taking Euler's formula but I can only get it to reduce down

$$\frac{-i-1}{\sqrt{2}i}$$

I have also tried converting to polar form, but I just really can't see how these two are equivalent.