Question

Mostre que o número complexo
(1+2i) (1-2i) e real

Answer 1

$(1 + 2i)(1 - 2i)\\\\= (1 + 2\sqrt{-1})(1 - 2\sqrt{-1})\\\\ = 1 - 2\sqrt{-1} + 2\sqrt{-1} -4\sqrt{-1} \times \sqrt{-1}\\\\ = 1 - 4(-1)\\\\ = 1 + 4\\\\ = 5$