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!

Homework Help: Complex number homework

  1. Jul 18, 2014 #1
    1. The problem.

    Given that z= 3-4i
    Show that z^2 = 3-4i

    Hence or otherwise find the roots of the equation (z+i)^2=3-4i

    2. My attempt.

    The first part of the problem is strait forward z^2= (2-i)(2-i) then expand to get the desired result.
    Now the second part

    (z+i)^2=3-4i. Becomes

    z^2+ 2zi+i^2 = 3-4i

    From here on I replace z with 2-i and get nowhere!
  2. jcsd
  3. Jul 18, 2014 #2


    User Avatar
    Gold Member

    Given that z= 3-4i
    leads to z² = -7-24i
    There must be a mistake in your statement.

    Besides that, the equation z²=3-4i has two solutions:

    z1=(2-i) and z2=-(2-i)

    Solving (z+i)²=3-4i is then straightforward.
  4. Jul 18, 2014 #3
    Yes there was a mistake! It should have read... Given that z = 2-i
  5. Jul 18, 2014 #4
    So you have (2 - i)2 = 3 - 4i and you are looking for roots for (x + i)2 = 3 - 4i (I've changed the unknown to x to avoid confusion).
  6. Jul 18, 2014 #5
    Yes! The variable z does confuse things a bit.
  7. Jul 18, 2014 #6


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Don't forget, if you use x this way it is possibly a complex number !
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted