Imaginary numbers

Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related?
What is its sum?

Correct answer:

Sum =  0

Step-by-step explanation:

Answer is a conjugate pair of imaginary numbers (its real parts is zero).
The two imaginary numbers that add up to a real number would be ni and -ni, because ni + (-ni) = ni - ni = 0; where 'n' is any real number, no zero. Thus, the sum of this two imaginary numbers become a real number 0.

$$\begin{gathered} ie\mathrm{.}\mathrm{.}\mathrm{.}\{3i;-3i\} \\ \mathrm{\Sigma }=3i+(-3i)=0 \end{gathered}$$

Try another example

Showing 1 comment:

Dr Math

add up a number and its conjugate

1 year ago  Like

Related math problems and questions:

• Linear imaginary equation
  Given that 2(z+i)=i(z+i) "this is z star" Find the value of the complex number z.
• De Moivre's formula
  There are two distinct complex numbers z, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers.
• The modulus
  Find the modulus of the complex number 2 + 5i
• Is complex
  Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
• Find the sum
  Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• Three numbers
  Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67.
• Fractions mul add sum
  To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
• Linear combination of complex
  If z1=5+3i and z2=4-2i, write the following in the form a+bi a) 4z1+6z2 b) z1*z2
• Three numbers
  We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
• Sum of odd numbers
  Find the sum of all odd integers from 13 to 781.
• David number
  Jana and David train the addition of the decimal numbers so that each of them will write a single number and these two numbers then add up. The last example was 11.11. David's number had the same number of digits before the decimal point, the Jane's numbe
• ABS CN
  Calculate the absolute value of complex number -15-29i.
• Two numbers
  Find the four times smaller number for numbers 12 and 36 and then add them.
• The sum
  The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?
• Goniometric form
  Determine the goniometric form of a complex number z = √ 110 +4 i.
• Sum 1-6
  Find the sum of the geometric progression 3, 15, 75,… to six terms.
• The sum
  The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.