Respuesta :
The other person was correct, but it wasn't in the form you would normally use.
The correct form of the answer is: [tex]-512\sqrt{3} +512i[/tex]
A complex number is a part of a number system that includes real numbers and imaginary units. The solution of the (2√3 + 2i)^5 is 512(i-√3).
What is a complex number?
A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i sometimes known as the imaginary unit, and which obeys the equation i² = -1.
The solution to the problem can be written as,
[tex](2 \sqrt{3} + 2i)^5\\\\\= (2 \sqrt{3} + 2i)^2 \times (2 \sqrt{3} + 2i)^2 \times (2 \sqrt{3} + 2i)\\\\=(12-4+8i\sqrt3) \times (12-4+8i\sqrt3) \times (2 \sqrt{3} + 2i)\\\\= (8+8\sqrt 3) \times (8+8\sqrt 3) \times (2 \sqrt{3} + 2i)\\\\= (8+8\sqrt3)^2 \times (2 \sqrt{3} + 2i)\\\\=(64-189+128\sqrt3)\times (2 \sqrt{3} + 2i)\\\\=(-128+128\sqrt3)\times (2 \sqrt{3} + 2i)\\\\= -256\sqrt3-256i+768i-256\sqrt3\\\\=-512\sqrt3+512i[/tex]
Hence, the solution of the (2√3 + 2i)^5 is 512(i-√3).
Learn more about Complex Numbers:
https://brainly.com/question/10251853
