Complex Numbers

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

What is the imaginary unit 'i'?

Back

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

Front

What does i^2 equal?

Back

i^2 equals -1.

Front

How do you multiply two complex numbers?

Back

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

Front

What is the sum of (5 - 2i) and (-7 + 8i)?

Back

The sum is -2 + 6i.

Front

How do you find the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.

Front

What is the modulus of a complex number?

Back

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

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 real part of a complex number?

Back

The real part of a complex number a + bi is 'a'.

Front

What is the imaginary part of a complex number?

Back

The imaginary part of a complex number a + bi is 'b'.