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