1)
`z_0=i^14=i^((3*4)+2)=i^2=-1;`
`z_3=5i*z_1=5i*(1-2i)=10+5i;`
`z_4=z_3/z_2=(10+5i)/(2+1i)=(10*2+5*1)/(2^2+1^2)+i*(2*5-10*1)/(2^2+1^2)=`
`=(20+5)/(4+1)+i*(10-10)/(4+1)=`
`=25/5+0/5i=5;`
`z_5=z_1*z_2=(1-2i)*(2+i)=2+i-4i-2i^2=4-3i;`
`z_6=4+3i;`
`z=z_0+z_6-z_4=(-1)+(4+3i)-(5)=-2+3i;`
2)
`z=-sqrt(2)+sqrt(2)i;|z|=sqrt(x^2+y^2)=sqrt((-sqrt(2))^2+(sqrt(2))^2)=sqrt(4)=2;`
`x=-sqrt(2); y=sqrt(2); =>x<0; y>0;phi=arg(z)=arctan((sqrt(2))/(-sqrt(2)))+pi=-pi/4+pi=(3*pi)/4=2.3562;`
`z=2*e^(i135^@)=2*e^(i(-pi/4+pi))=2*e^((3*pi)/4i)=2*e^(2.3562i)`
`z=(-sqrt(2)+sqrt(2)i)^7=2^7*e^((3*pi)/4*7i)=128*e^((21*pi)/4i)`
`z=2(cos((3*pi)/4)+i*sin((3*pi)/4))=2e^((3*pi)/4i);`
3)
`z=-125i;|z|=sqrt(x^2+y^2)=sqrt(0^2+(-125)^2)=sqrt(15625)=125;`
`x=0; y=-125; =>x=0; y<0;phi=arg(z)=arctan((-125)/0)=pi/2=-1.5708;`
`r=(125)^(1/3)=5;`
`w_0=5(cos((pi/2+0*2*pi)/3)+i*sin((pi/2+0*2*pi)/3))=4.3301+2.5i;`
`w_1=5(cos((pi/2+1*2*pi)/3)+i*sin((pi/2+1*2*pi)/3))=-4.3301+2.5i;`
`w_2=5(cos((pi/2+2*2*pi)/3)+i*sin((pi/2+2*2*pi)/3))=0-5i;`