Suppose that z4=z1+z2*z*4​=*z*1​+*z*2​.  What is the imaginary part of z4*z*4​?

To find the imaginary part of \( z_4 = z_1 + z_2 \), where \( z_1 = e^{-j\frac{\pi}{2}} \) and \( z_2 = e^{+j\pi} \), follow these steps:

### Step 1: Recall \( z_1 \) and \( z_2 \)
We previously found:
\[
z_1 = -j
\]
\[
z_2 = -1
\]

### Step 2: Calculate \( z_4 = z_1 + z_2 \)
Now, sum the two complex numbers:
\[
z_4 = (-j) + (-1) = -1 - j
\]

### Step 3: Identify the Imaginary Part of \( z_4 \)
The complex number \( z_4 = -1 - j \) has an imaginary part of \( -1 \).

### Answer
The imaginary part of \( z_4 \) is \( \boxed{-1} \).

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Would you like more details or explanations? Here are some related questions:

1. What is the real part of \( z_4 \)?
2. What is the magnitude of \( z_4 \)?
3. How would \( z_4 \) change if \( z_1 = e^{j\frac{\pi}{2}} \)?
4. Can you find the phase angle of \( z_4 \)?
5. What does the result imply about the geometric representation of \( z_4 \) in the complex plane?

**Tip:** When working with complex numbers, it's helpful to keep track of both the real and imaginary parts separately during calculations.

Learn how to calculate the imaginary part of complex numbers z1 and z2, given the formula z4 = z1 + z2. This problem explores complex numbers, imaginary parts, and addition of complex numbers. Suitable for advanced high school or college-level students.

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