consider the limit limzi z iArgiz a what walue does the lim

consider the limit lim_z--->i (|z| + iArg(iz)

a) what walue does the limit apprpach as z approaches i along the unit circle |z|=1 in the first quadrant?

b) in the second quadrant?

c) what can you say about the limit based on a and b?

Solution

|z|+iarg|iz)

When z =1, i|z|=i and arg (iz) = arg (i) =pi/4

Hence limit in the first quadrant is i+ipi/4

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b) II quadrant.

z = i+iarg(-i)=i-pi/4

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c) As they are not equal limit does not exist as z approaches i.