Please help me solve this question on complex number

This is the question I am stuck with. I tried to solve it as in image below.

I am not getting the correct answer. What mistake am I doing? Please help. Thank you

Thanks Adren, Thanks Nilabro for your answers. I want to know, can we solve this question by the same approach as I did? If yes, please tell how.

Answer

this rotation is decribed by :

$$R:z\mapsto e^{i\pi/4}(z-(1+2i))+1+2i$$

Hence :

$$R(3+4i)=\frac{\sqrt2}{2}(1+i)(2+2i)+1+2i=\boxed{1+2(1+\sqrt2)i}$$

It's worth to know that, in general, the rotation with angle $\theta$ (radians) around the point whose affix is $z_0$ is described by :

$$z\mapsto e^{i\theta}(z-z_0)+z_0$$