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Complex Numbers Basics

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Questions and Answers

The _____ part of a complex number is a multiple of the square root of -1

imaginary

____ numbers consist of a real part and an imaginary part

Complex

When a complex number has a zero imaginary part, it is purely _____

real

Match the following operations with their results in the algebra of complex numbers:

$3 + 2i$ = Addition of $2 + 3i$ and $1 - i$ $5i$ = Multiplication of $i$ and $5$ $-4 - 7i$ = Subtraction of $2 - 3i$ from $-6 - 4i$ $-8i$ = Multiplication of $2i$ and $-4$ Signup and view all the answers

Match the following expressions with their simplified forms in the algebra of complex numbers:

$3 + 2i$ = $(1 + i)^2$ $4 - 7i$ = $(2 - i)(3 + 2i)$ $-14 - 23i$ = $(5 - 4i)(3 + 7i)$ $25 + 0i$ = $(5i)^2$ Signup and view all the answers

Match the following properties with their descriptions in the algebra of complex numbers:

Commutative = The property that addition and multiplication of complex numbers can be done in any order Associative = The property that addition and multiplication of complex numbers can be regrouped in any order Distributive = The property that multiplication distributes over addition in complex numbers Identity element = The complex number that when added to or multiplied by any other complex number leaves it unchanged Signup and view all the answers

Study Notes

Complex Numbers

The imaginary part of a complex number is a multiple of the square root of -1
Complex numbers consist of a real part and an imaginary part
When a complex number has a zero imaginary part, it is purely real

Complex Number Operations

Match operations with their results in the algebra of complex numbers

Complex Number Expressions

Match expressions with their simplified forms in the algebra of complex numbers

Complex Number Properties

Match properties with their descriptions in the algebra of complex numbers

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Description

Test your knowledge about complex numbers, which consist of a real part and an imaginary part. Learn about the imaginary part being a multiple of the square root of -1, and how a complex number with a zero imaginary part is purely real.