Operations with Complex Numbers and Imaginary

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

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 value of i^2?

Back

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 add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Front

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

Back

The modulus of a complex number a + bi is given by √(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.

Front

What is the polar form of a complex number?

Back

The polar form of a complex number is expressed as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Front

How do you multiply two complex numbers?

Back

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