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 is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What does i^2 equal?

Back

i^2 = -1.

Front

How do you add complex numbers?

Back

To add complex numbers, add the real parts and the imaginary parts separately.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL) and apply the fact that i^2 = -1.

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 divide complex numbers?

Back

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.

Front

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

Back

The modulus of a complex number a + bi is given by √(a^2 + b^2).

Front

What is the argument of a complex number?

Back

The argument of a complex number is the angle θ in polar coordinates, given by θ = arctan(b/a).