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

2 years ago  Like

Related math problems and questions:

• Distance two imaginary numbs
  Find the distance between two complex number: z₁=(-8+i) and z₂=(-1+i).
• Conjugate equation
  Find the numbers of a and b, if (a - bi) (3 + 5i) is the Conjugate of (-6 - 24i)
• Linear imaginary equation
  Given that 2(z+i)=i(z+i) "this is z star" Find the value of the complex number z.
• Evaluate 18
  Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
• 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.
• An Argand diagram
  Find the sum z1+z2 and difference z1-z2 and z2-z1 of z1=5+2i and z2=2+3i by an Argand diagram.
• The modulus
  Find the modulus of the complex number 2 + 5i
• The sum 10
  The sum of three decimals are 938.629. Two of them are 456.54 and 392.69. Find the third one.
• Is complex
  Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
• 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.
• Find the sum
  Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• 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?
• Sum of 20
  Sum of the two numbers is 15 1/6. If one of the numbers is 2 2/3, find the other number.
• 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.
• Three unknown numbers
  The sum of of three numbers is 106. the first number is 10 more then the third. The second number is 2x the third. What are the numbers?