What is
ii ?
Formula:
z=a+i⋅bln(z)=ln(|z|)+i⋅Arg(z)Arg(z)=φln(a+i⋅b)=ln(√a2+b2)+i⋅arctan(ba)
ii=ei⋅ln(i)
z=i=0+i⋅1|a=0b=1ln(i)=ln(0+i⋅1)=ln(√02+12)+i⋅arctan(10)=ln(1)+i⋅arctan(10)|ln(1)=0=0+i⋅arctan(10)|arctan(10)=π2=0+i⋅π2=i⋅π2
ii=ei⋅ln(i)=ei⋅i⋅π2=ei2⋅π2|i2=−1=e−π2=0.20787957635…
What is
ii ?
Formula:
z=a+i⋅bln(z)=ln(|z|)+i⋅Arg(z)Arg(z)=φln(a+i⋅b)=ln(√a2+b2)+i⋅arctan(ba)
ii=ei⋅ln(i)
z=i=0+i⋅1|a=0b=1ln(i)=ln(0+i⋅1)=ln(√02+12)+i⋅arctan(10)=ln(1)+i⋅arctan(10)|ln(1)=0=0+i⋅arctan(10)|arctan(10)=π2=0+i⋅π2=i⋅π2
ii=ei⋅ln(i)=ei⋅i⋅π2=ei2⋅π2|i2=−1=e−π2=0.20787957635…