Question

1 - Calcule o Número Complexo:

(1+2i)³ =

Answer 1

(1+2i) ^ 2 . (1+2i)
(1+4i+4i^2).(1+2i)
(4i-3).(1+2i)
4i+8i^2-3-6i
-11-2i

Answer 2

$Como\; \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3,\;temos\\\\ \left(1+2i\right)^3 = 1^3+3\cdot \:1^2\cdot \:2i+3\cdot \:1\cdot \left(2i\right)^2+\left(2i\right)^3\\\\ = 1+1\cdot \:2\cdot \:3i+1\cdot \:3\left(2i\right)^2+\left(2i\right)^3\\\\ = 1+6i-12+\left(2i\right)^3\\\\ = 1+6i-12-8i\\\\ = -8i+6i+1-12\\\\ = -2i+1-12\\\\ = \framebox[1.5\width]{-11\:-\:2i}$