Adding and Subtracting Complex Numbers

Adding and Subtracting Complex Numbers Concept Explanation:

Complex numbers are in the form $z = a + bi$ , where $a$ is the real part, and $b$ is the imaginary part. Adding and subtracting complex numbers involves combining the real and imaginary parts separately:

To add $z_1 = a + bi$ and $z_2 = c + di$ , the result is:

$z_1 + z_2 = (a + c) + (b + d)i$

To subtract $z_1 = a + bi$ from $z_2 = c + di$ , the result is:

$z_1 - z_2 = (a - c) + (b - d)i$

Diagram:

A diagram illustrating the addition of two complex numbers in the complex plane:

Hard Questions:

Q1: Add $z_1 = 3 + 5i$ and $z_2 = 7 - 2i$ .

Step-by-Step Solution:

$z_1 + z_2 = (3 + 7) + (5 - 2)i = 10 + 3i$

Answer:

The sum is $10 + 3i$ .

Q2: Subtract $z_1 = 8 + 6i$ from $z_2 = 5 - 4i$ .

Step-by-Step Solution:

$z_2 - z_1 = (5 - 8) + (-4 - 6)i = -3 - 10i$

Answer:

The difference is $-3 - 10i$ .

Q3: Add $z_1 = -2 + 3i$ and $z_2 = 4 + 7i$ .

Step-by-Step Solution:

$z_1 + z_2 = (-2 + 4) + (3 + 7)i = 2 + 10i$

Answer:

The sum is $2 + 10i$ .

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