Complex Conjugates

Front

What are complex conjugates?

Back

Complex conjugates are pairs of complex numbers of the form a + bi and a - bi, where a and b are real numbers.

Front

How do you simplify a complex number?

Back

To simplify a complex number, combine like terms and express it in the form a + bi.

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result is a real number: (a + bi)(a - bi) = a^2 + b^2.

Front

What is the imaginary unit 'i'?

Back

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

Front

How do you add complex numbers?

Back

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

Front

How do you subtract complex numbers?

Back

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

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

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?

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 a + bi is the angle θ in polar coordinates, calculated as θ = arctan(b/a).