To simplify and express the given expression in the form $a - i b$, let’s clarify the components of the problem. It appears the question includes terms like $(t+i)z$, $r$, $r_r$, $r_z$, and $(2-i)$. I will assume the operations are multiplication and aim to express the result in the desired format. If you meant something else, please clarify.

Given: $(t + i)z \cdot r \cdot r_r \cdot r_z \cdot (2 - i)$

1. Group terms and work systematically:

   • Combine $(t + i)$ and $(2 - i)$ first: $(t + i)(2 - i) = t \cdot 2 - t \cdot i + 2 \cdot i - i^2$ Using $i^2 = -1$, this becomes: $2t - t \cdot i + 2 \cdot i + 1 = (2t + 1) + i(2 - t)$

2. Introduce $z$, $r$, $r_r$, and $r_z$: Multiply the result by $z \cdot r \cdot r_r \cdot r_z$. Let these terms collectively be represented as $C$, where: $C = z \cdot r \cdot r_r \cdot r_z$ The full expression becomes: $C \cdot \big((2t + 1) + i(2 - t)\big)$

3. Distribute $C$: Separate real and imaginary parts: $\text{Real part: } C(2t + 1), \quad \text{Imaginary part: } C(2 - t)$

4. Final result: $C \cdot (2t + 1) - iC \cdot (t - 2)$

Thus, the expression in the form $a - i b$ is: $a = C \cdot (2t + 1), \quad b = C \cdot (t - 2)$

Let me know if this interpretation aligns with your intent, or if any variable definitions or operations need clarification! 😊

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Follow-Up Questions:

1. Could you clarify the roles of $t, z, r, r_r, r_z$? Are they specific variables or functions?
2. Do you want further expansion of the terms $C = z \cdot r \cdot r_r \cdot r_z$?
3. Should I include examples of similar simplifications for practice?
4. Would you like to see a numerical example with specific values for these variables?
5. Do you need a graph or visualization of this expression?

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Tip:

When working with complex numbers, always simplify $i^2$ as $-1$ early to streamline calculations!