3

$(1-\sqrt3i)(1-i)^2 + 1 + \sqrt3i = ?$

My result is: $-2i - 2\sqrt3 + 1 + \sqrt3i$

Is this the right result or am I doing something wrong?

Thank you.

Sawarnik
  • 7,284
  • 7
  • 33
  • 74
Kurama
  • 49
  • 1
    You are correct, but the answer is still incomplete. The standard form for complex numbers is $a+bi$, so you should combine the real and the imaginary terms in the answer you have so far. – MJD Apr 09 '14 at 12:47

1 Answers1

3

$$(1-i\sqrt3)(1-i)^2+1+i\sqrt3=(1-i\sqrt3)(-2i)+1+i\sqrt3=$$

$$=-2\sqrt3-2i+1+i\sqrt3=(1-2\sqrt3)+(\sqrt3-2)i$$

DonAntonio
  • 211,718
  • 17
  • 136
  • 287
  • 2
    @MJD; how can it "engage"(?) if the work isn't shown? And the answer does answer the OP's question: his solution is wrong. I show him the different steps taken, so that he can check his own work. – DonAntonio Apr 09 '14 at 12:50
  • 3
    Hmmm...and after writing nicely the OP's question I can see now his solution is right, after all. And @MJD, why did you delete your comment to my answer explaining your downvote? – DonAntonio Apr 09 '14 at 12:52
  • I decided that my previous practice of downvoting without leaving explanatory comments was better, since it invariably leads to unproductive arguments like this one. – MJD Apr 09 '14 at 12:56
  • @MJD "Unproductive" meaning that someone doesn't agree with you? Oh, well: I see. – DonAntonio Apr 09 '14 at 12:57
  • My pleasure, @Kurama – DonAntonio Apr 09 '14 at 13:00