Complex Numbers

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.

Front

What does the letter 'i' represent in complex numbers?

Back

The letter 'i' represents the imaginary unit, which is defined as the square root of -1.

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

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

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a² + b²). It represents the distance from the origin to the point (a, b) in the complex plane.

Front

How do you divide two complex numbers?

Back

To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, (a + bi) / (c + di) = [(a + bi)(c - di)] / [(c + di)(c - di)].

Front

What is the real part of a complex number?

Back

The real part of a complex number a + bi is the value 'a'. It is the component that does not involve the imaginary unit 'i'.

Front

What is the imaginary part of a complex number?

Back

The imaginary part of a complex number a + bi is the value 'b'. It is the coefficient of the imaginary unit 'i'.