a=7\pi /4\\\\z=\sqrt{2}(cos7\pi /4 +i*sin7\pi /4)\\\\z^4=(1-i)^4=(\sqrt{2})^4(cos4*7\pi /4+i*sin4*7\pi /4)=\\=4(cos7\pi + i*sin7\pi )=4(-1+i*0)=-4" alt="(1-i)^4-?\\\\|z=1-i\\|z|=\sqrt{1^2+(-1)^2}-\sqrt{1+1}=\sqrt{2}\\\\(cosa=1/\sqrt{2}=\sqrt{2}/2, sina=-1/\sqrt{2}=-\sqrt{2}/2)=> a=7\pi /4\\\\z=\sqrt{2}(cos7\pi /4 +i*sin7\pi /4)\\\\z^4=(1-i)^4=(\sqrt{2})^4(cos4*7\pi /4+i*sin4*7\pi /4)=\\=4(cos7\pi + i*sin7\pi )=4(-1+i*0)=-4" align="absmiddle" class="latex-formula">