Alg2CP Complex Numbers Check-Up

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 the square root of -1.

Front

How do you simplify the square root of a negative number?

Back

To simplify the square root of a negative number, factor out -1 to express it as a real number multiplied by the imaginary unit i. For example, √(-x) = i√x.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square roots of negative numbers.

Front

How do you multiply complex numbers?

Back

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

Front

What is the result of multiplying i by itself?

Back

The result of multiplying i by itself is i^2 = -1.

Front

How do you add complex numbers?

Back

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

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.

Front

How do you divide complex numbers?

Back

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

Front

What is the result of (a + bi) - (c + di)?

Back

The result is (a - c) + (b - d)i, which combines the real and imaginary parts.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by |a + bi| = √(a^2 + b^2). It represents the distance from the origin in the complex plane.