2023 - 2024 - Complex Numbers Operations

Front

Define a complex number.

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as i² = -1.

Front

What is the imaginary unit 'i'?

Back

Front

How do you add two complex numbers?

Back

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

Front

Simplify the expression: (12 - 4i) + (-2 + 8i)

Back

10 + 4i.

Front

How do you subtract two complex numbers?

Back

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

Front

Simplify the expression: (5 + 4i) - (-1 - 2i)

Back

6 + 6i.

Front

What is the result of multiplying two imaginary numbers?

Back

The product of two imaginary numbers is a real number. For example, i * i = i² = -1.

Front

Simplify the expression: 3i(3i - 4)

Back

-9 - 12i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi².