Convert the complex number from polar form to rectangular form, $a+b i$. \[ 5.9\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) \] The rectangular form is

Step 1 ：Given the complex number in polar form is \(5.9\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)\)

Step 2 ：We need to convert this to rectangular form, which is given by \(r\cos \theta + r i \sin \theta\), where \(r = 5.9\) and \(\theta = \frac{2\pi}{3}\)

Step 3 ：Calculate the real part, \(r\cos \theta\), which gives \(-2.95\)

Step 4 ：Calculate the imaginary part, \(r i \sin \theta\), which gives \(5.11i\)

Step 5 ：Add the real and imaginary parts to get the rectangular form of the complex number

Step 6 ：Final Answer: The rectangular form of the complex number is \(\boxed{-2.95 + 5.11i}\)