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, defined as the square root of -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

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

What is the product of two complex numbers (a + bi)(c + di)?

Back

The product is given by (ac - bd) + (ad + bc)i.

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 multiply complex numbers?

Back

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

Front

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

Back

The modulus is given by |a + bi| = √(a² + b²).

Front

How do you divide complex numbers?

Back

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, (a + bi) / (c + di) = [(a + bi)(c - di)] / (c² + d²).

Front

What is the real part of a complex number a + bi?

Back

The real part is 'a'.

Front

What is the imaginary part of a complex number a + bi?

Back

The imaginary part is 'b'.