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The given problem asks to simplify the following complex number into an imaginary number:

\[
z_2 = \sqrt{-676} + \sqrt[3]{-1331} - \sqrt[5]{(-7)^5} + \sqrt[3]{(-64)^2}
\]

### Let's break this down step by step:

1. **First term: \( \sqrt{-676} \)**
   \[
   \sqrt{-676} = \sqrt{676} \cdot \sqrt{-1} = 26i
   \]
   where \( i \) is the imaginary unit.

2. **Second term: \( \sqrt[3]{-1331} \)**
   \[
   \sqrt[3]{-1331} = -\sqrt[3]{1331} = -11
   \]

3. **Third term: \( \sqrt[5]{(-7)^5} \)**
   \[
   \sqrt[5]{(-7)^5} = -7
   \]

4. **Fourth term: \( \sqrt[3]{(-64)^2} \)**
   \[
   (-64)^2 = 4096 \quad \Rightarrow \quad \sqrt[3]{4096} = \sqrt[3]{16^3} = 16
   \]

### Now, summing these terms together:
\[
z_2 = 26i + (-11) + (-7) + 16
\]
Simplifying the real terms:
\[
z_2 = 26i + (-11 - 7 + 16) = 26i - 2
\]

Thus, the simplified form of the complex number is:
\[
z_2 = 26i - 2
\]

To make it purely imaginary, we would disregard the real part \( -2 \), and the imaginary part is \( 26i \).

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Would you like further details or have any questions?

### Related Questions:
1. How do you simplify other types of complex numbers?
2. What is the significance of the imaginary unit \( i \)?
3. How do cube roots of negative numbers work in complex numbers?
4. Can you explain higher-order roots, such as fifth roots, in more detail?
5. What are the properties of imaginary and complex numbers in general?

### Tip:
Always check the roots carefully, especially for negative radicands, as they often involve the imaginary unit \( i \).

Sederhanakanlah bilangan kompleks di berikut ini menjadi bilangan imajiner: z2 = √-676 + ³√-1331 - ⁵√(-7)⁵ + ³√(-64)²

Learn how to simplify complex numbers involving square roots and cube roots of negative numbers. This example demonstrates key concepts in complex numbers and imaginary units, perfect for high school students in Grade 11-12.

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