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To solve this problem, we need to find the angle (or argument) of the complex number \( z = -8.6 - j2.9 \) in radians.

The argument \( \theta \) of a complex number \( z = a + jb \) is given by:

\[
\theta = \text{atan2}(b, a)
\]

Where:
- \( a \) is the real part of \( z \) (in this case, \( -8.6 \))
- \( b \) is the imaginary part of \( z \) (in this case, \( -2.9 \))

Using the formula:

\[
\theta = \text{atan2}(-2.9, -8.6)
\]

Let's compute this.The angle (or argument) of the complex number \( z = -8.6 - j2.9 \) in radians is approximately \( -2.82 \) radians.

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How do you convert this angle to degrees?
2. What is the modulus (magnitude) of the complex number \( z \)?
3. How would you write \( z \) in polar form?
4. How does the quadrant of \( z \) affect the argument?
5. What would the argument be if \( z = -8.6 + j2.9 \)?

**Tip:** The function \( \text{atan2}(y, x) \) is useful because it automatically handles the signs of both components to return the correct angle in the correct quadrant.

¿Cuál es el ángulo en radianes del siguiente número complejo? z = -8.6 - j2.9

This problem involves calculating the argument (or angle) of the complex number z = -8.6 - j2.9 in radians using the atan2 function. Learn about complex numbers and how to use polar coordinates in this step-by-step solution suitable for students in Grades 10-12.

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