need help with complex numbers

Question

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

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

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

Thank you.

Answer 1

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

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