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We are given the complex numbers \( z_1 = 1 + i \) and \( z_2 = 5 \) (after simplification). We need to find a complex number \( w = a + bi \) such that \( w z_1 = z_2 \).

The equation \( w z_1 = z_2 \) simplifies to \( w = \frac{z_2}{z_1} \), which leads to the solution \( a = \frac{5}{2} \) and \( b = -\frac{5}{2} \).

Thus, the complex number \( w \) is:

\[
w = \frac{5}{2} - \frac{5}{2}i
\]

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Here are 5 related questions:
1. How do you divide complex numbers?
2. What is the geometric interpretation of multiplying complex numbers?
3. How can you express the conjugate of a complex number?
4. What are the properties of complex number multiplication?
5. How do you find the modulus of a complex number?

**Tip:** When solving for a complex number, it can help to express both sides in the form \( a + bi \) to simplify the comparison of real and imaginary parts.

Given: z1 = 1 + i and z2 = 4(2 + 3i) - 3(1 + 4i). Find a complex number w, written in the form w = a + bi, such that wz1 = z2 and then find w̅. Choose the correct value for w̅ from the list below.

Learn how to find a complex number w such that wz1 = z2, and compute the conjugate w̅. This problem covers key concepts such as complex number multiplication, division, and properties of conjugates. Suitable for undergraduate mathematics.

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