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`        Find the fourth root of of -16i`
7 years ago

510 Points
```										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

```
7 years ago
Arjit Srivastava
32 Points
```										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!
```
7 years ago
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