# Too Complex to Solve!

Algebra Level 3

Let $$z=a+bi$$, $$|z|=5$$, and $$b>0$$. If the distance between $$(1+2i)z^3$$ and $$z^5$$ is as large as possible, then determine $$z^4$$. Give your answer as the sum of the real and imaginary parts of $$z^4$$.

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