Question

what is the fourth root of 1+i2

Answer 1

Answer:

Fourth root of 1 is ±1

Fourth root of 16 is ±2

Fourth root of 81 is ±3

Fourth root of 256 is ±4

Fourth root of 625 is ±5

Fourth root of 1296 is ±6

Fourth root of 2401 is ±7

Fourth root of 4096 is ±8

Fourth root of 6561 is ±9

Fourth root of 10000 is ±10

De Moivre's Theorem

for k = 0, 1, ..., n-1

1–√n=cos2kπn+sin2kπni

−1−−−√n=cos(2k+1)πn+sin(2k+1)πni

Fourth Root of a Negative Number

Find the fourth root of negative 81 with n=4 for the 4th root.

Solution:

−81−−−−√4

=81−−√4⋅−1−−−√4

=8114⋅(−1)14

Using DeMoivre's Theorem we get the equation

=8114⋅(cos((2k+1)π4)+sin((2k+1)π4)i)

Solving our equation for k=0 to k=n-1 (for k = 0, 1, 2 and 3);

The roots of −81−−−−√4 are:

2.12132034+2.12132034i

−2.12132034+2.12132034i

−2.12132034−2.12132034i

2.12132034−2.12132034i

Answer 2

Answer:

root 1/2

Step-by-step explanation: