The given expression is:

$3\left( \cos \frac{\pi}{2} + i \sin \frac{\pi}{2} \right)$

This represents a complex number in polar form. To convert this into rectangular form (i.e., $a + bi$ where $a$ is the real part and $b$ is the imaginary part), we will evaluate the trigonometric functions and simplify.

1. $\cos \frac{\pi}{2} = 0$
2. $\sin \frac{\pi}{2} = 1$

Substituting these values into the expression:

$3 \left( 0 + i \cdot 1 \right) = 3i$

Thus, the complex number in rectangular form is:

$\boxed{3i}$

Would you like more details or have any questions? Here are some follow-up questions for further exploration:

1. What is the relationship between polar and rectangular forms of complex numbers?
2. How would the expression change if the angle were $\pi$ instead of $\frac{\pi}{2}$?
3. Can you explain how Euler's formula relates to this problem?
4. What are the applications of complex numbers in polar form?
5. How do you plot a complex number in both polar and rectangular coordinates?

Tip: In polar form, the real part corresponds to $r \cos \theta$, and the imaginary part corresponds to $r \sin \theta$, where $r$ is the magnitude, and $\theta$ is the angle.