Adding and Subtracting Complex Numbers

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i² = -1.

Front

How do you add complex numbers?

Back

To add complex numbers, you add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, you subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is the result of (3 + 4i) + (2 + 5i)?

Back

The result is (3 + 2) + (4 + 5)i = 5 + 9i.

Front

What is the result of (6 + 2i) - (4 + 3i)?

Back

The result is (6 - 4) + (2 - 3)i = 2 - 1i.

Front

What is the value of i²?

Back

The value of i² is -1.

Front

What is the result of 5i + 10i?

Back

The result is (5 + 10)i = 15i.

Front

How do you simplify the expression 3i - 5i?

Back

You simplify it by subtracting the imaginary parts: 3i - 5i = -2i.

Front

What is the result of -6i - 2i?

Back

The result is -6i - 2i = -8i.