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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.

Write the complex number in rectangular form: 3(cos(π/2) + i sin(π/2))

Learn how to convert the complex number 3(cos(π/2) + i sin(π/2)) from polar to rectangular form. This solution includes the use of trigonometric functions and Euler's formula. Suitable for high school students studying complex numbers.

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