- #1

- 302

- 1

**1. Find the solution of the following**

(w)^4 = 1

w can be a complex number (in polar form)

w^n = re^jntheta (0 <= theta < 2pie)

1 = 1e^j(2pie*k) k = 0, 1, 2 ,3 .........

equating the two

----------------------------------------

r = 1

theta*n = 2pie*k

theta = 2pie*k/n

for k = 0 theta = 0

for k = 1 theta = 2pie/4

for k = 2 theta = 4pie/4

for k = 3 theta = 6pie/4

so there are 4 roots with magnitude 1 and the angles above.

NOW im confused on how would I apply a similar approach to a question like the following:

(w - (1+ j2))^5 = (32/sqrt(2))(1 + j)

Any help appreciated!

(w)^4 = 1

w can be a complex number (in polar form)

w^n = re^jntheta (0 <= theta < 2pie)

1 = 1e^j(2pie*k) k = 0, 1, 2 ,3 .........

equating the two

----------------------------------------

r = 1

theta*n = 2pie*k

theta = 2pie*k/n

for k = 0 theta = 0

for k = 1 theta = 2pie/4

for k = 2 theta = 4pie/4

for k = 3 theta = 6pie/4

so there are 4 roots with magnitude 1 and the angles above.

NOW im confused on how would I apply a similar approach to a question like the following:

(w - (1+ j2))^5 = (32/sqrt(2))(1 + j)

Any help appreciated!

Last edited: