what is (4+3i)^4

Question

I got -527+336i but I can't figure out how to get that answer.

Answer 1

One way is to use the binomial theorem determining the format for (a + b)⁴. Then substitute 4 for a and 3i for b.

(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴.

Another method: (4+3i)² (4+3i)². Since (4+3i)² = 16 +24i - 9 = 7+24i,, the final result comes from (7+24i)².This does indeed yield an answer of -527 + 336i.