BENAR	SALAH
z1 + z2 = 2 + i	
z1 x z2 = 2 + 4i	
z2 + z3 = 1 + i	
z1 - z3 = 1 + i	
z1 + z2 = 2 + i	
z1 x z2 = 2 + 4i	
z2 + z3 = 1 + i	
z1 - z3 = 1 + i

Based on the information you've provided, we will assume that \( z_1 \), \( z_2 \), and \( z_3 \) are complex numbers, and we are asked to verify the equations.

Let's summarize the given equations for clarity:

1. \( z_1 + z_2 = 2 + i \)
2. \( z_1 \times z_2 = 2 + 4i \)
3. \( z_2 + z_3 = 1 + i \)
4. \( z_1 - z_3 = 1 + i \)

We will attempt to verify the truth of these equations by solving for \( z_1 \), \( z_2 \), and \( z_3 \).

### Step 1: Solving for \( z_1 \) and \( z_2 \) from equations 1 and 2
From the first equation:
\[
z_1 + z_2 = 2 + i
\]

From the second equation:
\[
z_1 \times z_2 = 2 + 4i
\]

This forms a system of equations. To solve for \( z_1 \) and \( z_2 \), we can express one variable in terms of the other and substitute it.

### Step 2: Solving for \( z_3 \)
From the third equation:
\[
z_2 + z_3 = 1 + i
\]
This allows us to express \( z_3 \) in terms of \( z_2 \):
\[
z_3 = 1 + i - z_2
\]

We also have the fourth equation:
\[
z_1 - z_3 = 1 + i
\]
Substituting \( z_3 \) into this equation gives:
\[
z_1 - (1 + i - z_2) = 1 + i
\]

### Conclusion:
We can solve these equations using algebraic methods to verify whether the given equalities hold. However, without further clarification or the specific values for \( z_1 \), \( z_2 \), and \( z_3 \), I cannot definitively say whether they are true or false at this stage. Let me know if you'd like to proceed with solving for these variables step by step.

---

Would you like to continue solving this system, or do you have further details for the values of \( z_1 \), \( z_2 \), and \( z_3 \)?

Here are 5 related questions you might want to explore:
1. How do we solve systems of equations involving complex numbers?
2. What methods can be used to factor or expand complex number expressions?
3. How can the modulus and argument of a complex number be found?
4. What are the properties of complex number multiplication and addition?
5. How do we visualize complex numbers geometrically?

**Tip:** When working with complex numbers, remember that addition and multiplication follow similar rules to real numbers, but you must keep track of the imaginary unit \( i \), where \( i^2 = -1 \).

BENAR SALAH z1 + z2 = 2 + i z1 x z2 = 2 + 4i z2 + z3 = 1 + i z1 - z3 = 1 + i

Explore the solution for a system of equations involving complex numbers: z1 + z2 = 2 + i, z1 × z2 = 2 + 4i, z2 + z3 = 1 + i, and z1 - z3 = 1 + i. Learn key concepts in algebra and complex numbers suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation