Operations with Imaginary Numbers Part 1

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is 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 is a complex number?

Back

A complex number is a number that has a real part and an imaginary part, expressed in the form a + bi, where a is the real part and b is the imaginary part.

Front

What is the real part of a complex number?

Back

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

Front

What is the imaginary part of a complex number?

Back

The imaginary part of a complex number a + bi is the value 'b', which is multiplied by the imaginary unit 'i'.

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

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL). For example, (a + bi)(c + di) = ac + adi + bci + bdi². Remember that i² = -1.

Front

What is the result of i(2 + 5i)?

Back

The result is -5 + 2i.

Front

What is the result of (2 + 3i)(4 - 2i)?

Back

The result is 14 + 8i.