Question

1. A expressão (1 + i√3)^2. (√3 + i)^2 é igual a
a) -16
b)-12
c)-4
d)-1
e)1

Answer 1

$(1 + i\sqrt{3} )^2 * (\sqrt{3} + i)^2\\(a + b)^2 = a^2 + 2ab + b^2\\(1 + i\sqrt{3} )^2 = 1 + 2i\sqrt{3} + (i\sqrt{3})^2 = 1 + 2i\sqrt{3} + 3(-1) = - 2 + 2\sqrt{3}i \\(\sqrt{3} + i )^2 = 3 + 2\sqrt{3} i + i^2 = 2 + 2\sqrt{3}i\\(- 2 + 2\sqrt{3}i)(2 + 2\sqrt{3}i) = (-2 * 2 - 2\sqrt{3}*2\sqrt{3}) + (-2 * 2\sqrt{3} + 2\sqrt{3} * 2)i\\(-4 - 4(3)) + (-4\sqrt{3} + 4\sqrt{3})i = (-16) + (0)i = -16$