Question

write the complex number (3+4i)^7 in the form A+iB​

Answer 1

Answer:2916 + 2401i

Step-by-step explanation:(a+bi)ⁿ = aⁿ + naⁿ-1b + (n*(n-1)/2!)aⁿ-2b² + ... + bⁿ

Plugging in the values, we get:

(3+4i)⁷ = 3⁷ + 73⁶4i + (7*6/2!)3⁵4²i² + ... + 4⁷i⁷

We can simplify this as follows:

(3+4i)⁷ = 2187 + 2401i - 729i²

Since i² = -1, we can simplify this to:

(3+4i)⁷ = 2187 + 2401i + 729

(3+4i)⁷ = 2916 + 2401i

Thus, (3+4i)⁷ = 2916 + 2401i, which is in the form of a + ib.