Complex Numbers Practice

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

What is the product of two imaginary numbers, (i)(3i)?

Back

The product is -3, since (i)(3i) = 3(i^2) = 3(-1) = -3.

Front

What is the product of (2i)(3i)?

Back

The product is -6, since (2i)(3i) = 6(i^2) = 6(-1) = -6.

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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

How do you add two complex numbers, such as (2 + 3i) and (4 + 5i)?

Back

To add, combine the real parts and the imaginary parts: (2 + 3i) + (4 + 5i) = (2 + 4) + (3i + 5i) = 6 + 8i.

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How do you multiply two complex numbers, such as (1 + 2i) and (3 + 4i)?

Back

Use the distributive property: (1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i^2 = 3 + 10i - 8 = -5 + 10i.