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 significance of complex conjugates in division?

Back

Complex conjugates are used to eliminate the imaginary part in the denominator when dividing complex numbers.

Front

Simplify: (4 + 3i) + (2 - 5i)

Back

6 - 2i.

Front

Simplify: (3 + 4i) - (1 + 2i)

Back

2 + 2i.

Front

What is the formula for the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a² + b²).

Front

How do you express a complex number in polar form?

Back

A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Front

What is the argument of a complex number?

Back

The argument of a complex number a + bi is the angle θ formed with the positive x-axis, calculated as θ = arctan(b/a).

Front

Simplify: (2 + 3i)(2 - 3i)

Back

The result is 13.