Complex Number Operations

Front

What is 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 i^2 = -1.

Front

How do you add complex numbers?

Back

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

Front

Back

Front

How do you subtract complex numbers?

Back

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

Front

Back

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and remember that i^2 = -1.

Front

Back

Front

What is the imaginary unit?

Back

The imaginary unit, denoted as i, is defined as the square root of -1, meaning i^2 = -1.

Front

Back

Front

How do you find the sum of two complex numbers?

Back

To find the sum, add the real parts and the imaginary parts separately. For example, for (a + bi) + (c + di), the sum is (a + c) + (b + d)i.