Question

calcule: módulos dos complexos |(1+2i)^6|

Answer 1

Bom dia

l(1 + 2i)⁶l = l117 + 44il 

lzl = √(117² + 44²) 
lzl = √(13689 + 1936)
lzl = √15625

lzl = 125 

Answer 2

(1+2i)⁶=[(1+2i)²]³

(1+2i)²=1+4i-4=4i-3

(4i-3)³=(4i)³-3*(4i)²*3+3*(4i)*3²-3³

(4i-3)³=-64i+144+108i-27

(4i-3)³=117+44i

|(1+2i)⁶| =√(117²+44²)

|(1+2i)⁶| =√(117²+44²)

=√15625

= 125