1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Number Question (Easy)

  1. May 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Verify that i2=-1
    (a+bi)(c+di) = (ac-bd)(ad+bc)i

    2. Relevant equations
    (a+bi)(c+di) = (ac-bd)(ad+bc)i

    3. The attempt at a solution
    I tried choosing coefficients so that it would be (i)(i) = (0 - 1)+(0+0)i = -1
    so then I get i^2 = -1

    But I was told that this was wrong and to try again...

    Can anyone explain what I did was wrong or if
    theirs a smarter way to verify?
  2. jcsd
  3. May 6, 2016 #2


    User Avatar
    Homework Helper

    We define i as the root of -1. So $$i^2 = -1$$ is true, no need to verify this.

    The following statement is false: $$(a+bi)(c+di) = (ac-bd)(ad+bc)i$$
    This would mean that the product of 2 complex numbers is an imaginary number. This is false. For example, $$i * i = i^2 = -1$$ is a real number.

    What is $$(a+bi)(c+di)$$ equal to, using distributivity and $$i^2 = -1$$
    Last edited: May 6, 2016
  4. May 6, 2016 #3


    Staff: Mentor

    Are you sure that you have written the equation above correctly? As already noted by Math_QED, this is false.
  5. May 6, 2016 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It's supposed to be:

    ##(a+bi)(c+di) = (ac-bd) + (ad+bc)i##

    And, assuming this holds for all ##a, b, c, d## show that ##i^2 = -1##.

    That's what I assume the exercise to be.
  6. May 7, 2016 #5


    Staff: Mentor

    But the whole point of this exercise is to prove this. In other words, the OP can't use this definition.

    Let's sit back and see what the OP says...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted