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# Which Pair Of Complex Numbers Has A Real-Number Product? All Answers

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## Can the product of two complex numbers be a real number?

The product of the complex number and its conjugate is a real number! This is true in general, since (a+bi) \times (a-bi)=a^2+b^2 and a and b are always real numbers.

## What is a real number complex numbers?

Real numbers include all decimal fractional, negative, and positive integers, whereas the Complex number can be written as the sum or difference of a real number and imaginary number, include numbers like 4 – 2i or 6+√6i.

### Which pair of complex numbers has a real-number product?A 1 + 3i6iB 1 + 3i2 – 3iC 1 + 3i

Which pair of complex numbers has a real-number product?A 1 + 3i6iB 1 + 3i2 – 3iC 1 + 3i
Which pair of complex numbers has a real-number product?A 1 + 3i6iB 1 + 3i2 – 3iC 1 + 3i

## Do the complex numbers contain the real numbers?

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra. They can be applied to many aspects of real life, especially in electronics and electromagnetism.

## Is the product of two complex numbers is always a complex number?

Therefore, product of two complex numbers is a complex number. Note: Product of more than two complex numbers is also a complex number. (iii) z ∙ 1 = z = 1 ∙ z, so 1 acts as the multiplicative identity for the set of complex numbers.

## What is the product of 2 complex numbers?

Multiplication of complex numbers is a process of the multiplication of two or more complex numbers using the distributive property. Mathematically, if we have two complex numbers z = a + ib and w = c + id, then multiplication of complex numbers z and w is written as zw = (a + ib) (c + id).

## What is a real number product?

The sum or product of two real numbers is the same regardless of their order. Identity Properties. The sum of a real number and 0 is that real number. The product of a real number and 1 is that real number.

## Is 6i a real number?

Examples: 3+6i (3 is the real part, 6i is the imaginary part)

## See some more details on the topic which pair of complex numbers has a real-number product? here:

### Algebra 2 – Unit Test Review Flashcards | Quizlet

Which pair of complex numbers has a real-number product? C. (1 + 3i)(1 – 3i). Solve for mc014-1.jpg in the equation mc014-2.jpg.

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### Which pair of complex numbers has a real number product | Yang Apa

BEST ANSWER GETS A METAL!!!! Which pair of complex numbers has a real-number product? (1 + 3i)(6i) (1 + 3i)(2 – 3i)

### Best answer gets a which pair of complex numbers has a real …

implementation of distribution property. (1 + 3i) (6i) = 1 * 6i + 3i * 6i. -18 + 6i ——> is not a real number. therefore. case A is not a real number product …

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## Is 5 3i a real number?

Step-by-step explanation:

it is not true that 5-3i is a real number. 5 is a real number.

## Is 7i a real number?

An imaginary number is any number of the form bi, where b is real (but not 0) and i is the square root of −1.
Complex Number Real part Imaginary part
3 + 7i 3 7i
18 – 32i 18 −32i

## Is complex number subset of real numbers?

(In fact, the real numbers are a subset of the complex numbers-any real number r can be written as r + 0i, which is a complex representation.) Complex numbers are an important part of algebra, and they do have relevance to such things as solutions to polynomial equations.

## Is the square of a complex number always a real number?

The absolute square of a complex number is calculated by multiplying it by its complex conjugate. This give the magnitude squared of the complex number. The absolute square is always real. We will use complex exponentials all the time.

## Is 2 a complex number?

For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Examples.
Complex Number Real Number Imaginary Number
-1+2i -1 2i
7-9i 7 -9i
-6i 0 -6i (Purely Imaginary)
6 6 0i (Purely Real)
6 thg 6, 2020

### Complex Numbers as Ordered Pairs of Real Numbers | Chapter 1 | FSc Part 1 | Math’s Humor

Complex Numbers as Ordered Pairs of Real Numbers | Chapter 1 | FSc Part 1 | Math’s Humor
Complex Numbers as Ordered Pairs of Real Numbers | Chapter 1 | FSc Part 1 | Math’s Humor

## Is the difference between two real numbers a real number?

The difference of two real numbers is always a real number. The product of two real numbers is always a real number. The quotient of two real numbers is always a real number.

## What is the product of the complex numbers (- 3i 4 and 3i 4?

The product of the complex numbers (-3i + 4) and (3i + 4) is 25.

## What is the product of a complex number and its conjugate?

This always happens when a complex number is multiplied by its conjugate – the result is real number. Once again, we have multiplied a complex number by its conjugate and the answer is a real number. This is a very important property which applies to every complex conjugate pair of numbers.

## What is the product of complex conjugates?

The product of a complex number with its conjugate is equal to the square of the number’s modulus: This allows easy computation of the multiplicative inverse of a complex number given in rectangular coordinates: as well.

## Is 2 a real number?

These are the set of all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, ……. ∞. Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

## What is the product of 2/3 and 4?

The product of -2,3 and 4 is -24. hope it will help you. please mark it as brainliest.

## How do you find a product?

In mathematics, a product is a number or a quantity obtained by multiplying two or more numbers together. For example: 4 × 7 = 28 Here, the number 28 is called the product of 4 and 7. As another example, the product of 6 and 4 is 24, because 6 times 4 is 24.

## What is 6i as a complex number?

Calculation steps

Absolute value: abs(6i) = |6i| = √02 + 62 = 6. The absolute value of a complex number (also called the modulus) is a distance between the origin (zero) and the image of a complex number in the complex plane.

## What is 2i?

2i is an imaginary number because it has the form ‘bi’ Remember, ‘i’ is the imaginary unit and is equal to the square root of -1. Even though ‘i’ is NOT a variable, we can multiply it as if it were. So i • i gives us i2. Squaring √ (-1) cancels out the square root, leaving us with just -1.

## What is real and complex?

A real number can be a rational and irrational number and can have any value on the number line. A complex number exists in the form a + ib where i is used for denoting the imaginary part and a and b denote the real numbers. These numbers can be plotted on the number line.

## Under what conditions will the product of two complex numbers always be a purely imaginary number?

Answer. The sum of two complex numbers is a pure imaginary number when either of the two conditions happen: The real parts of two complex numbers are both zero. The real parts of two complex numbers have the same absolute value but have different signs.

### Complex Numbers – Practice Problems

Complex Numbers – Practice Problems
Complex Numbers – Practice Problems

## Which statement must be true about the complex numbers?

Which statement must be true about the complex numbers? The complex numbers have opposite real numbers.

## What is a conjugate of an imaginary number?

You find the complex conjugate simply by changing the sign of the imaginary part of the complex number. Example. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 – 7i.

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