Complex Numbers Notes Flashcard

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 √-1.

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1.

Front

What is the result of √-1?

Back

The result of √-1 is i.

Front

How do you simplify √(-a) where a > 0?

Back

√(-a) can be simplified to i√a.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.

Front

How do you add two complex numbers (a + bi) and (c + di)?

Back

To add two complex numbers, combine the real parts and the imaginary parts: (a + c) + (b + d)i.

Front

How do you multiply two complex numbers (a + bi) and (c + di)?

Back

To multiply two complex numbers, use the distributive property: (ac - bd) + (ad + bc)i.

Front

What is the modulus of a complex number a + bi?

Back

The modulus of a complex number a + bi is √(a² + b²).

Front

What is the argument of a complex number?

Back

The argument of a complex number is the angle θ formed with the positive x-axis in the complex plane, often calculated using tan(θ) = b/a.