Find the square roots of i
would the modulus = i ? and not sure how to work out its argument?
any help apprecited
First, what made you think, originally, that there were four square roots of i?
Second, while the modulus of z= i is 1, its argument is NOT [itex]\pi/4[/itex]. I don't know where you got that "1" in " ". Surely you don't think argument is the arctangent of the modulus? The argument of "a+ bi" is the arctangent of b/a, if a is not 0. Of course, if a= 0 then a+ bi= bi which has modulus if b> 0, if b< 0. (0 has no "argument").
So if z= i, . HALF of that is and half of is . Those are the arguments of the two square roots of i which, of course, have modulus , so the two square roots are and .