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Find the fourth root of of -16i

Find the fourth root of of -16i

Grade:11

2 Answers

vikas askiitian expert
509 Points
11 years ago

let Z is the fourth root of  of -16i

  Z= (-16i)1/4

   ={(16)(-1)(i) }1/4

    ={  16i3 }1/4                          (i2 =-1)

     =2 {( (i)4 )3/16 }                     (i4 =1)

      Z=2

 

 

Arjit Srivastava
32 Points
11 years ago

Actually, its complex. And there are four of them. And each one has an imaginary component equal in magnitude to its real components magnitude, because they lie on the y = x and y = -x lines, 45° incline/decline from the x(real)-axis and each root is therefore 90° rotated from the next. 4th root of -16 = ±√2 ± i√2. Anyway, if you take a purely positive real number and find its fourth root, you will get both positive and negative, purely real and purely imaginary roots. If you take a positive or negative, pure imaginary or real number and raised it to the fourth power, it will be a positive real number.

So, the only option for a fourth root of a negative real would be elsewhere on the complex plane. I hope this sheds some light on your question. I know it doesn't answer it directly as you intended it, but maybe helps you somewhat with it!

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