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Q. The values of $(16)^{1 / 4}$ are

Complex Numbers and Quadratic Equations

Solution:

We have
$(16)^{1 / 4} =\left(2^{4}\right)^{1 / 4}=2(1)^{1 / 4} $
$=2(\cos 0+i \sin 0)^{1 / 4}$
$=2\left\{\cos \frac{1}{4}(2 k \pi+0)+i \sin \frac{1}{4}(2 k \pi+0)\right\},$
$k = 0, 1, 2, 3$
$=2 \times 1,2 \times i, 2 \times-1,2 \times-i=\pm 2, \pm 2 i$