- #1
E_Q
- 15
- 0
When doing FP1 ages ago I discovered a way to seemingly get i3=±i, and since then nobody has provided a proper explanation for why the positive solution is impossible.
Standard solution
i3=i2.i
=-1.i
=-i
'flawed' solution
i3=(√-1)3
=√(-1)3 Using the laws of surds, √a.√b=√ab
=±√-1
=±i
Of course, this applies to i2 just as well:
i2=√-1.√-1
=±√1
=±1
I'm not really suggesting the method is flawed, just is gives an incorrect answer as well as the correct one. I'm familiar with this (from solving modulus graphs, for example), but can't understand why the positive solution is incorrect in this case.
Thanks for any help!
Standard solution
i3=i2.i
=-1.i
=-i
'flawed' solution
i3=(√-1)3
=√(-1)3 Using the laws of surds, √a.√b=√ab
=±√-1
=±i
Of course, this applies to i2 just as well:
i2=√-1.√-1
=±√1
=±1
I'm not really suggesting the method is flawed, just is gives an incorrect answer as well as the correct one. I'm familiar with this (from solving modulus graphs, for example), but can't understand why the positive solution is incorrect in this case.
Thanks for any help!