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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

### Images related to the topicWhich 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:

### Which pair of complex numbers has a real-number product?

Answer: .

### 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.

### 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 …

## 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?

…

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?

**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) |

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

### Images related to the topicComplex 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| = **√0 ^{2} + 6^{2} = 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 i^{2}. 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

### Images related to the topicComplex 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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