Dividing complex numbers review (article) | Khan Academy (2024)

Review your complex number division skills.

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  • ZardinTheTreeAtlas

    5 years agoPosted 5 years ago. Direct link to ZardinTheTreeAtlas's post “What do I do when I have ...”

    What do I do when I have a problem like this : 3 / 2+i
    The "3" is over the "2+i".

    I don't know what to do and nothing will explain.

    (12 votes)

    • Polina Vitić

      5 years agoPosted 5 years ago. Direct link to Polina Vitić's post “Here's a hint: you need t...”

      Dividing complex numbers review (article) | Khan Academy (4)

      Dividing complex numbers review (article) | Khan Academy (5)

      Here's a hint: you need to "rationalize" the denominator. When you see 2+i in the denominator, what you really have is 2 + √(-1)

      To rationalize the denominator, try this:

      3/(2+i) · (2-i)/(2-i)
      = 3/(2+√(-1)) · (2-i)/(2-√(-1))
      ...and so on.

      Try working this out, and please let me know if you have any more questions.

      Hope this helps!

      (29 votes)

  • Matthew Johnson

    4 years agoPosted 4 years ago. Direct link to Matthew Johnson's post “What would be a real worl...”

    What would be a real world application where imaginary numbers would be involved in practical applications? Fractal geometry is excluded!

    (8 votes)

  • Kyra

    7 years agoPosted 7 years ago. Direct link to Kyra's post “Hello, The equation from ...”

    Hello, The equation from a review question i did was: 6-6i/8+2i. The answer I got was: 60/68 -60i/68 BUT the professor's solution was: 9/17 -15i/17. How am I wrong? :(

    (3 votes)

    • Kim Seidel

      Multiply the numerator & denominator by the conjugate of 8+2i = 8-2i
      (6-6i)(8-2i) / (8+2i)(8-2i)
      Numerator: (6-6i)(8-2i) = 48 -12i -48i -12 = 36 - 60i
      -- looks like you got +12, rather than -12. Here the details: -6i(-2i) = 12i^2 = 12(-1) = -12
      Denominator: (8+2i)(8-2i) = 64 -16i +16i + 4 = 68
      Put the pieces back together: 36/68 - 60i/68
      Reduce the fractions by 4: 9/17 -15i/17
      Hope this helps

      (3 votes)

  • Tatiana

    2 years agoPosted 2 years ago. Direct link to Tatiana's post “I'm very comfortable rati...”

    I'm very comfortable rationalizing the denominator, but am still confused as to the reason we do this. Is the reason simply because we're trying to simplify the quotient as much as possible and it's not "clean" to have complex terms in the denominator?

    (1 vote)

    • Kim Seidel

      2 years agoPosted 2 years ago. Direct link to Kim Seidel's post “Rationalizing the denomin...”

      Rationalizing the denominator makes the denominator an integer. And, this makes it easier to do other math operations with the fraction. For example, if you need to add/subtract fractions, it is easier to find a common denominator working with integers than working with denominators that are irrational numbers.

      (7 votes)

  • Maximus

    a year agoPosted a year ago. Direct link to Maximus's post “It seems to follow from t...”

    It seems to follow from the proof that the product of a complex number and it's conjugate is a natural number; is that correct?

    (3 votes)

    • Kim Seidel

      a year agoPosted a year ago. Direct link to Kim Seidel's post “Natural numbers are: 1, 2...”

      Natural numbers are: 1, 2, 3, 4, 5, 6, ...
      The product of a complex number and its conjugate would create a real number. The set of real numbers includes: natural numbers, whole numbers, integers, rational numbers and irrational numbers.

      (2 votes)

  • connerking2

    5 years agoPosted 5 years ago. Direct link to connerking2's post “What if the equation has ...”

    What if the equation has more than 1i in the numerator?

    (2 votes)

    • Rae Riddle

      5 years agoPosted 5 years ago. Direct link to Rae Riddle's post “Then you need to simplify...”

      Then you need to simplify the numerator first, by combining like terms and simplifying any i exponents you might have.

      (2 votes)

  • HJKNAPP

    8 months agoPosted 8 months ago. Direct link to HJKNAPP's post “What do I do when I have ...”

    What do I do when I have a problem like (-5+1/2i). I can't multiply by the conjugate of the denominator without the denominator becoming 0. I nee help. Can Sal please post a video on this.

    (2 votes)

    • Kim Seidel

      8 months agoPosted 8 months ago. Direct link to Kim Seidel's post “How do you get 0? I'm as...”

      How do you get 0? I'm assuming your denominator is (-5+1/2i). It's not clear from what you have written as you have no fraction to show the numerator vs denominator.

      Anyway... The conjugate for (-5+1/2i) would be (-5-1/2i)
      Your denominator becomes (-5)^2-(1/2i)^2
      Simplify to get: 25-0.25i^2 = 25-0.25(-1) = 25+0.25 = 25.25
      There is no 0.

      Hope this helps.

      (1 vote)

  • Grace Wyatt

    5 years agoPosted 5 years ago. Direct link to Grace Wyatt's post “what if its just 12/5i? I...”

    what if its just 12/5i? I'm not sure what to do.

    (2 votes)

    • Kim Seidel

      5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “I believe you need to mul...”

      I believe you need to multiply by (-i)/(-i). This will eliminate the "i" in the denominator.
      Hope this helps.

      (1 vote)

  • Maryam shoukat

    3 years agoPosted 3 years ago. Direct link to Maryam shoukat's post “can you tell me the more ...”

    can you tell me the more power of i till 90power

    (1 vote)

  • poetrade314

    2 years agoPosted 2 years ago. Direct link to poetrade314's post “Hello everyone, Khan acad...”

    Hello everyone, Khan academy is great for learning, I appreciate!

    I have a question:
    determine the number z if u = 4 - 3i

    a) z/u = 0,4+0,8i
    please and thank U....

    I did so > z / 4-3i = 0,4+0,8i

    z = 0,4+0,8i (4-3i) but something is wrong I wanna understanding everything in every part-...

    (0 votes)

    • cossine

      2 years agoPosted 2 years ago. Direct link to cossine's post “Remember to use brackets...”

      Remember to use brackets

      z/u = 0.4+0.8i # I presume there was some keyboard issue don't use "," in place of a decimal point

      => z = u(0.4+0.8i)

      (2 votes)

Dividing complex numbers review (article) | Khan Academy (2024)

FAQs

What is the division rule for complex numbers? ›

Formula for Dividing Complex Numbers

The quotient a + ib/c + id represents the division of two complex numbers z1 = a + ib and z2 = c + id. This is determined using the z1/z2 = ac + bd/c2 + d2 + i (bc – ad / c2 + d2) formula for division of complex numbers.

What is a complex number divided by its conjugate? ›

Technically, you can't divide complex numbers — in the traditional sense. You divide complex numbers by writing the division problem as a fraction and then multiplying the numerator and denominator by a conjugate. The conjugate of the complex number a + bi is a – bi. The product of (a + bi)(a – bi) is a2 + b2.

How do you simplify i in the denominator? ›

Answer and Explanation:

To remove the imaginary number from the denominator, we multiply the numerator and denominator by the conjugate of the denominator.

How do you solve complex numbers easily? ›

Add or subtract the real parts and then the imaginary parts. Example 2: Add: ( 3 − 4 i ) + ( 2 + 5 i ) . Solution: Add the real parts and then add the imaginary parts. To subtract complex numbers, subtract the real parts and subtract the imaginary parts.

What are the rules for complex numbers? ›

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

What is the argument of the division of complex numbers? ›

The argument of the quotient of two complex numbers is found by subtracting the argument of the denominator from the argument of the numerator. If you're dividing z1 by z2, then arg(z1/z2) = arg(z1) - arg(z2).

Are the complex numbers an algebra? ›

A Complex Number is an algebraic expression that contains the factor i= -1. These numbers are divided into two parts: the real part, denoted by Re(z), and the imaginary part, denoted by I(z). For the complex number represented by 'z,' the imaginary part is denoted by im(z).

What does z mean in complex numbers? ›

Z=a+ib, where a,b ∈ R and i is an imaginary number, is used to denote a complex number. Z is the conjugate of Z in the complex number system. A complex number's conjugate is another complex number with the same real portion as the original and an imaginary part that has the same magnitude but a different sign.

What does w mean in complex numbers? ›

w generally indicates a cube root of unity in complex numbers.

How do you simplify the denominator? ›

When there is more than one term under a radical sign in the denominator, it becomes a bit trickier. To simplify, you will need to multiply the numerator and denominator by the denominator's conjugate. The conjugate is the same expression but with the opposite sign in the middle.

What is an example of a complex fraction? ›

A complex fraction is a fraction that contains one or more fractions in either the numerator or denominator, or both. For example, 2/3 is a simple fraction, but (2/3)/(4/5) is a complex fraction. Complex fractions can be written in various ways, including using horizontal or vertical bars, brackets, or parentheses.

How do you divide big numbers step by step? ›

We'll use 845 ÷ 3 to walk through this step-by-step process:
  1. Set up the problem. Write the dividend (845) under the division bar and the divisor (3) outside the bar.
  2. Divide. ...
  3. Multiply. ...
  4. Subtract. ...
  5. Bring down the next digit. ...
  6. Repeat the steps. ...
  7. The final answer with a remainder. ...
  8. Convert the remainder to decimal form.
Feb 6, 2024

How to divide two complex numbers in polar form? ›

We can divide two complex numbers in polar form by dividing their moduli and subtracting their arguments.

How do you divide compound numbers? ›

Dividing a Mixed Number by Another Mixed Number

First, convert both mixed numbers to improper fractions. Then, take the reciprocal of the second fraction and multiply it with the first fraction. Finally, simplify the answer you get and convert it into a mixed number if required.

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