Answer:
[tex]\large\boxed{x=-3i}[/tex]
Step-by-step explanation:
[tex](x-i)^5=32(x+i)^5\\\\(x-i)^5=2^5(x+i)^5\qquad\text{use}\ (ab)^n=a^nb^n\\\\(x-i)^5=\bigg(2(x+i)\bigg)^5\iff x-i=2(x+i)\qquad\text{use distributive property}\\\\x-i=2x+2i\qquad\text{add}\ i\ \text{to both sides}\\\\x=2x+3i\qquad\text{subtract 2x from both sides}\\\\-x=3i\qquad\text{chnage the signs}\\\\x=-3i[/tex]
