The equation for a complex number \( X = -1 + 5i \) in its simplest form is just \( X = -1 + 5i \). This represents a point in the complex plane, where:

- The real part is \(-1\),
- The imaginary part is \(5i\) (where \( i \) is the imaginary unit, \( i = \sqrt{-1} \)).

### Key interpretations:
1. **Standard Form (Algebraic)**: \( X = a + bi \), where \( a = -1 \) and \( b = 5 \).
2. **Polar Form**: You can also express it in polar form as \( X = r(\cos \theta + i \sin \theta) \), where:
   - \( r = \sqrt{(-1)^2 + (5)^2} = \sqrt{26} \),
   - \( \theta = \tan^{-1}\left(\frac{5}{-1}\right) \).
   We can compute this if you need more detail.

Would you like more information on the polar form or related concepts?

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### Related Questions:
1. How do you convert a complex number from standard to polar form?
2. What is the significance of the real and imaginary parts in a complex number?
3. How do you perform operations (addition, subtraction) with complex numbers?
4. How do you find the conjugate of a complex number?
5. What is the geometric interpretation of a complex number in the complex plane?

**Tip**: When dealing with complex numbers, always remember the identity \( i^2 = -1 \), as it simplifies many expressions.

Understand the equation of the complex number X = -1 + 5i, with its standard and polar forms. Learn how to calculate the magnitude and argument using algebraic and trigonometric concepts. Suitable for students in Grades 10-12.

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