The numbers \( x = -3 + 3i \) and \( x = -3 - 3i \) are **complex** numbers.

A complex number is of the form \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit defined by \( i^2 = -1 \). In your case:
- \( x = -3 + 3i \) has a real part \( -3 \) and an imaginary part \( 3i \),
- \( x = -3 - 3i \) has a real part \( -3 \) and an imaginary part \( -3i \).

Neither of these numbers is purely real because they both contain an imaginary component.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What are the real and imaginary parts of a complex number?
2. How do you add or subtract complex numbers?
3. How do you multiply complex numbers?
4. What is the modulus of a complex number?
5. How do you represent complex numbers graphically?

**Tip:** To convert a complex number into polar form, you can use the modulus and argument of the number.

Explore the nature of complex numbers through the example x = -3 + 3i and x = -3 - 3i. This topic covers key concepts in complex number algebra, identifying real and imaginary parts, and distinguishing between complex and real numbers. Suitable for Grades 9-12.

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