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Manipal MET2013MathematicsComplex Number

If i z^4+1=0 , then z can take the value

Options

  1. A1+1 2
  2. B8 +i 8
  3. C1 4 i
  4. Di

Correct answer

B. 8 +i 8

Step-by-step solution

i z^4=-1 array ll & z^4=- 1 i & z^4=i & z=(i)^ 1 / 4 =(0+i)^ 1 / 4 & z= ( 2 +i 2 )^ 1 / 4 & z= 8 +i 8 array (using De Moirrels theorem)

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