Two complex numbers have a product of 30 and positive integers as real parts. Write all possible combinations of such numbers.

, , ,

, and .

Step-by-step explanation:

Given that two complex numbers have a product of 30 and the real part of the complex numbers are positive integers.

Let one complex number is where is a positive integer and is a real number.

As the product of two complex numbers is a purely real number, so the other complex number must be the conjugate of the first complex number.

So, another complex number

As a product of both the numbers = 30

[as i^2=-1]

Now, as a is a positive integer, so by taking possible values of a, we can determine the values of b from the equation (i).

For

The positive sign is for the one number and the negative sign is for the conjugate number (another number).

So, the 1st combination is

Similarly,

For

So, the 2nd combination is

For

So, the 3rd combination is

For

So, the 4th combination is

For

So, the 5th combination is

The higher integral value of is not possible for any real .

Hence, the possible combinations of required numbers are

, , ,

, and .

a

step-by-step explanation:

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3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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