1.

Find the value of (– 16)1/4

Answer»

(–16) = 16(–1) = 16(cosπ + isinπ)

= 24(cos(2k + 1)π + isin(2k + 1)π], k ∈ z

(–16)1/4 = (24)1/4[cos(2k + 1)π + i sin (2k + 1)π]1/4

= 2cos(2k + 1)π/4, k = 0, 1, 2, 3

The value of (–16)1/4 is

2cos(2k + 1)π/4, k = 0, 1, 2, 3



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