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 i = √(-1).

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.

Front

How do you add complex numbers?

Back

To add complex numbers, combine their real parts and their 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 their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

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

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, combine like terms.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of the quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you solve a quadratic equation with complex roots?

Back

To solve a quadratic equation with complex roots, use the quadratic formula. If the discriminant is negative, the solutions will include imaginary numbers.