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# Complex Numbers Basics

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.

Created by
@AccurateEclipse

imaginary

Complex

real

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

<p>$3 + 2i$ = 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 $-4$</p> Signup and view all the answers

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

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

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

<p>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</p> 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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