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Which Expression Is Equivalent To (4 + 7i)(3 + 4i)?

Addition and subtraction are the two basic math operations. While both add and subtract positive numbers, only subtraction is useful when dealing with small numbers such as a budget or plan.

When adding large numbers such as purchases or remodel jobs, it is best to use the basic addition form. This is equivalent to adding one item into another item with no intervening items.

The basic form can be converted into other added-item forms by changing the size of the items to be added, or by changing how they are numbered. Both of these techniques are covered in this article.

This article will discuss how to give new life to old-fashioned subtraction problems by using the equivalent added-item forms.

Put expressions into a common denominator

When two expressions have the same effect, put them into a common denominator. For example, adding 4 to 7 and 3 to 4 yields a common denominator of 12.

Common denominators like 12 help enterers understand which addition or subtraction and multiplication or division algorithm is used for an expression.

In the example above, 3 + 4 = 9, so 3 + 9 = 13 is a valid expression. However, adding 4 to 7 and then dividing that answer by 3 yields an answer of 1.1, which is not equal to 9.

Identify like terms

When you look up a word or phrase, your computer looks at how similar words and phrases are. When two words or phrases are very similar, your computer considers them like terms.

Like terms describe each other using the same words or modified words. The term hairstyle describes the term hairstyle, but not directly.

When you look up a word or phrase, the computer compares it to other similar-looking words and phrases. When two similar-looking words describe an object or event, they consider them like terms.

These like terms describe each other using the same words or modified ones. The term hairstyle describes the term hairstyle, but not directly.

When you look up a word or phrase, the computer compares it to other similar-looking words and finds those with more appearances (like terms). When two are similar, they merge into one.

Calculate the greatest common factor (GCF)

The greatest common factor (GCF) is a useful math concept that has both common and complex meanings. Very little of the time, you will understand what the GCF means, but when you do, it can be very powerful.

When two numbers are equal, their GCF is 1. If two numbers are not equal, then the GCQ (greatest remainder) is not necessarily 0. The GCF can be bigger or smaller than 0, making it a useful concept to know.

The GCF can be found by dividing each number by the other. For example, if the first number is 4 and the second number is 7, then the first number divided by 7 gives you 2 and the second number divided by 7 gives you 8.

So, the greatest common factor of 2 and 8 is 4×7.

Combine like terms

When there are many like terms in a term or phrase, it is common to combine them into a one-term or one-explanation term or explanation.

For example, when studying calculus, we learn that the output of an calculus function is always positive. Therefore, the equivalent of adding and subtracting in terms of positive is interchangeably called subtraction and addition.

Similarly, when studying trigonometry, we learn that all measurements in trigonometry are measured in degrees. Therefore, the equivalent of measuring a diagonals in terms of degrees is measuring a angle in degrees.

We can do this with both square root and hypotension.

Express one fraction in terms of the other

Adding and subtracting fractions is one of the most common ways to calculate with numerals. Numerals add and subtract fractions, so when calculating with them, you can use any order for addition or subtraction.

When solving problems using addition or subtraction, be sure to use the right expression for the fraction. For example, using a fraction with a value of 6 that has a half: (6 + 5) / 2 = 6 + (6 * 2) / 4 = 16.

When solving problems with multiplication or division, be sure to use the correct multiple and/or fraction for the whole.

Swap fractions to different sides of an equation

When there is an equation with more than one term in it, there is a chance to change the order in which those terms are presented.

Using the previous example, swap the (4 + 7i) and (3 + 4i) elements into new equations:

(8 + 3i)÷2=0, so (4 + 7i) replaces (3 + 4i). Similarly, when (7 + i) replaces (3), then (4 + 7i) must go away.

This is called a swap or a change of grid style. There are two kinds of grid style: linear and relief. Linear styles show equal length of all elements in an equation, while relief shows a longer period of one element per row and one element per column.
Whether a shift in grid style creates different problems or not depends on the content inside them.

Use a trig substitution formula

When a substitution formula is needed for a trig function, the formula can be found in a math book or in a computer program.

In the case of the addition and subtraction functions, for example, there are two different tables of values for each function. One is called the normal table, and the other is called the trigonometric table.

The trigonometric table includes functions like sin (the sine function), cos (the cosine function), tan (the tangent function), atan (the arctangent function), and cosec (the alternating sine and cosine).

The normal table does not include functions that are not positive, negative, or even integer! It does have one exception to: radians. In that case, it has another table that does have those values.

Use the unit circle

The unit circle is a conceptually simple way to think about space. It’s a circle that represents any area of space. In fact, the unit circle is larger than the area of all but one point on a circle.

The pointy end of the unit circle represents locations in space that are relatively small. The floor-leveled portion of the unit circle represents locations that are large.

In between these two ends of the unit circle, there is no difference in terms of representation or size.


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