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To determine which quadrant the complex number \(5 + 17i\) is located in, let’s analyze the components:

1. The complex number \(5 + 17i\) can be written in the form \(a + bi\), where:
   - \(a = 5\), which is the real part.
   - \(b = 17\), which is the imaginary part.

2. On the complex plane:
   - The real part (\(a\)) determines the horizontal movement. Since \(5\) is positive, it moves to the right.
   - The imaginary part (\(b\)) determines the vertical movement. Since \(17\) is positive, it moves upwards.

3. In terms of quadrants:
   - Quadrant I is where both the real and imaginary parts are positive.

Since both \(5\) (real part) and \(17\) (imaginary part) are positive, \(5 + 17i\) is in **Quadrant I**.

### Answer: 
**Quadrant I**

Would you like more details or have any questions?

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### Related Questions:
1. What is the quadrant for the complex number \(-5 + 17i\)?
2. How do you plot complex numbers on the complex plane?
3. Can a complex number be on the boundary of a quadrant?
4. How do the signs of the real and imaginary parts affect the quadrant placement?
5. What is the modulus of the complex number \(5 + 17i\)?

### Tip:
When identifying the quadrant for a complex number, remember that the sign of the real part determines left or right, and the sign of the imaginary part determines up or down.

When graphing on the complex plane, which quadrant will the complex number 5 + 17i be found in?

Discover how to determine the quadrant for the complex number 5 + 17i on the complex plane. Learn about complex numbers, quadrants, and coordinate systems in this example, perfect for high school students.

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