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Question

If a=1+i2+i4++i2n and b=cos1(11+i), where i=1, then the value of tan(ba) is
  1. cannot be determined
  2. depends on the value of b 
  3. 0
  4. 1


Solution

The correct option is A cannot be determined
a=1+i2+i4++i2na=11+11++(1)n 
So, there are two values of a depending on n.
When n is odd, a=0
When n is even, a=1

Now, b=cos1(11+i)=cos1(1i2)
b=cos112=π4

When a=0, tan(ba) cannot be determined.
When a=1tan(ba)=1
Hence, the value of tan(ba) cannot be determined.

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