(2+2i)^5(-3+3i)^3 / (√3+1)^10?

Question

Convert all complex #'s to trigonometric form & simplify. Write answers in standard form.

Answer 1

Looks like a nice homework problem to me. But there are way too many steps in the answer to be worth just 10pts. How about this:
2+2i has radius
sqrt(2^2 +2^2)=sqrt(8)
and angle with
tan (angle)=2/2=1, i.e. angle=45 degrees.

Now, (2+2i)^5 will have radius sqrt(8)^5=2^(15/2) and angle 5*45=225 degrees.

You can now do the rest. Don't forget to subtract the angles when you do division!

Answer 2

It relies upon on how your instructor asks you the thank you to try this difficulty, yet yet or you're able to do it is to alter your mixed numbers into unsuitable fractions (one fraction) so 2 2/3 is 8/3 and 3 3/4 is 15/4 Now do what you probably did formerly by making use of looking someone-friendly denominator. 8/3 will become 32/12 15/4 will become 40 5/12 32/12 + 40 5/12 = seventy seven/12 you may discover that there isn't any extensive kind that is going into seventy seven and 12 nicely, so what you're able to do is take 12 and take it into seventy seven. so which you get an answer of 6 5/12 What you probably did isn't incorrect, however the formating is incorrect, and you probably did be conscious some thing is humorous. In you answer 17/12, the numerator is greater advantageous than the denominator, so which you would be able to make that fraction as a million 5/12 you in addition to mght have a 5, so 5 + a million 5/12 that makes 6 5/12. Now curiously like it relatively is been decreased.

Answer 3

I guess this isn't trigonometric form, but it's another way to get answers:

(2 * (-3) (1 + i) (1 - i)) ^ 3 = -12^3 = -1728
4 * (1 + i)^2 = 8i
(root3 + 1)^2 = 4 + 2root3
(root3 + 1)^8 = (28 + 16root3)^2 = 1552 + 896root3
(root3 + 1)^10 = 11584 + 6688root3

Putting it all together:
(2+2i)^2 ( -6 (1 + i) (1 - i) )^3 / (root3 + 1)^10 =
-i 13824 / (11584 + 6688root3) =
-i 432 / (362 + 209root3) =

Final Answer: -i 432 (362 - 209root3)

Answer 4

2+2i= 2sqrt2 < pi/4so (2+2i)^5 =2^7sqrt2<5pi/4
-3+3i= 3sqrt2<3pi/4 so (-3+3i)^3= 27*2^3/2 sqrt3+1)^10= 2^10 (I´ll suppose you mean (sqrt3+i)=2 so(sqrt3+i)^10= 2^10 <5pi/3
so
=2^7sqrt2*27*2^3/2 <3pi/2 /2^10 <5pi/3 = 27/2 <-pi/6
=27/2(sqrt3 / 2-1/2 i)=27/4(sqrt3-i)