Understanding the Quadratic Formula

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What is the term 'imaginary number' used to refer to?

A complex number with a real part equal to 0 (correct)

A rational number (fraction) that is an extension of the integers

An extension of the real numbers

A derogatory term for numbers regarded as fictitious or useless

Why were imaginary numbers initially called 'imaginary'?

They are just extensions of the real numbers

They were regarded by some as fictitious or useless (correct)

They have some properties that are different from the numbers previously worked with

They are an extension of the real numbers

What does a complex number with a real part equal to 0 look like?

$a + 0i$

$bi$ (correct)

$a + bi$

$a - bi$

What led to the naming of 'Real Numbers'?

'Real' because they were not Imaginary Signup and view all the answers

How are imaginary numbers similar to rational numbers (fractions)?

They are both extensions of other number sets Signup and view all the answers

Match the following mathematical concepts with their descriptions:

Imaginary numbers = Complex numbers with a real part equal to 0 Real numbers = Numbers not regarded as fictitious or useless Complex numbers = Numbers of the form a + bi Rational numbers = Extensions of the integers, such as fractions Signup and view all the answers

Match the following historical terms with their meanings:

Derogatory term = Coined in the 17th century to describe imaginary numbers Common denominator = Rule for adding fractions with different denominators Linear equations = Equations that can be plotted as straight lines on a graph Standard form = A specific way of writing linear equations Signup and view all the answers

Match the following mathematical terms with their explanations:

Quadratic formula = Formula used to find the roots of a quadratic equation Client-side scripting = Scripting language executed by the user's web browser Database queries = Commands used to retrieve specific information from a database Styling web pages = Process of applying visual design to web documents Signup and view all the answers

Match the following number types with their characteristics:

Fractions = Numbers expressed as one integer divided by another Integers = Positive and negative whole numbers, including zero Whole numbers = Non-negative integers, including zero Complex numbers = Numbers of the form a + bi, where a and b are real numbers Signup and view all the answers

Match the following mathematical terms with their origins:

Real numbers = Named 'real' because they were not imaginary Imaginary numbers = Initially regarded as fictitious or useless Complex numbers = Include both real and imaginary components Rational numbers = Developed as extensions of the integers, like fractions Signup and view all the answers