Let z

To convert the complex number $z = 6.48e^{2.86i}$ into its Cartesian form, we need to express it in terms of its real and imaginary components using Euler's formula:
$e^{ix} = \cos(x) + i\sin(x)$

Given $z = 6.48e^{2.86i}$: $z = 6.48(\cos(2.86) + i\sin(2.86))$

Now, let's calculate the values of $\cos(2.86)$ and $\sin(2.86)$:

1. Calculate $\cos(2.86)$
2. Calculate $\sin(2.86)$
3. Multiply these results by the modulus $6.48$

Let's compute these values.The Cartesian form of $z$ is: $z = -6.22 + 1.80i$

Would you like more details or have any questions?

Here are some related questions you might be interested in:

1. How do you convert a complex number from Cartesian to polar form?
2. What is Euler's formula and how is it used in complex numbers?
3. How do you multiply and divide complex numbers in polar form?
4. What are the geometric interpretations of complex numbers in polar and Cartesian forms?
5. How can you find the magnitude and argument of a complex number?

Tip: When converting complex numbers between forms, using a calculator or software for trigonometric calculations can help ensure accuracy.