Question

confuseddd!

Answer 1

i solved the problem and i got 31.98+0.877i but my online homework says that its wrong D:

Answer 2

multiply the angle by 5!!

Answer 3

Is this a graded assignment?

Answer 4

i did! look

Answer 5

\[(r(\cos(\theta)+i\sin(\theta))^n=r^n(\cos(n\theta)+i\sin(n\theta))\]

Answer 6

2^5(cos(5.pi/10)+isin(5.pi/10)

Answer 7

ok so you have
\[2^5(\cos(\frac{\pi}{2})+i\sin(\frac{\pi}{2}))\] right?

Answer 8

32(cos1571)+isin(1.571)= 32(0.9996)+0.0274i=31.98+0.8768i

Answer 9

so all you need now is
\[2^5=32\] and
\[\cos(\frac{\pi}{2})=?\]

Answer 10

its pi/10 not 2

Answer 11

put degrees out of your mind. you are working with numbers

Answer 12

\[5\times \frac{\pi}{10}=\frac{\pi}{2}\]

Answer 13

oh ! my bad

Answer 14

now it is easy right?

Answer 15

yeah

Answer 16

whew!

Answer 17

haha thank you! i need help with finding the fourth roots of 256

Answer 18

someone explained me but that's not what im looking for

Answer 19

all four of them right?

Answer 20

yeah like i know the last steps but i dont know to get to the equation, for instance i have this example that i did at school -8+8i , i dont know how to find the r and the angle to have the equation

Answer 21

we can do it the snap way, first find all four roots of 1, then find the fourth roots of 256
one we know already, one fourth root of 256 is 4

Answer 22

ok lets go slowly, but first note that finding the fourth roots of 256 in not like finding the roots of \(-8+8i\) because 256 is real

Answer 23

oh yeah

Answer 24

so all we have to do is find the fourth roots of 1, and then multiply each result by 4

Answer 25

we get two right away, since \(4^4=256\) and also \((-4)^4=256\)

Answer 26

which is like saying \(i^4=1\) and \((-1)^4=1\)

Answer 27

do you know the other two fourth roots of 1?

Answer 28

no

Answer 29

draw a unit circle, you know 1 is one answer so divide up in to 4 equal parts

Answer 30

\[1^4=1,i^4=1,(-1)^4=1,(-i)^4=1\] there are the four answers
\[\{1,i,-1,-i\}\] distributed evenly about the unit circle in the complex plane

Answer 31

so if i want the 4 "fourth roots" of any number, take those four numbers and multiply by the positive real fourth root
for example if i want the fourth roots of 81 i would instantly say: 3, 3i, -3, -3i

Answer 32

why 3?

Answer 33

oh never mind

Answer 34

because
\[3^4=81\]

Answer 35

easy right?

Answer 36

yes very haha but im still having problem with the other question the one of cos1/2 , it still says that its wrong