Question

How do you find (2+4i)^3 in rectangular form?

Answer 1

$(2+4i)^3=8+48i-96-64i=-88-16i$

Answer 2

note that (a + b)³ = a³ + 3a²b + 3ab² + b³

(2 + 4i)³ ← with a = 2 and b = 4i noting that i² = (√-1)² = -1

= 2³ + (3 × 4 × 4i ) + ( 3 × 2 × 16i² ) + ( 4i )³

= 8 + 48i  - 96 - 64i

= - 88 - 16i