Few questions about Pre Calc

So I'm taking this practice test and there are only a few questions left. I don't really understand them, so if you could help me out to the best of your knowledge, that would be great.

http://oi52.tinypic.com/11hs6d3.jpg
Here is the image of the question im having troubles on. I had to screen shot them because of certain symbols.

1)

1 - i represent it as on the fourth quadrant.

tan(θ) = y/x ====> tan(θ) = -1/1 ====> θ = tan^-1( - 1 ) =====> θ = [ 2π - π/4 = 7π/4 ]

I r I = √( 1^2 + (-1)^2 ) = √(1 + 1 ) = √(2)

r * e^(i * θ) =====> √(2) * e^(i * (7π/4) )

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2)

f(z) = z + i & z_0 = 1

z_0 = 1
z_1 = (1) + i = 1 + i
z_2 = (1 + i) + i = 1 + i + i = 1 + 2i
z_3 = (1 + 2i) + i = 1 + 2i + i = 1 + 3i

1 , 1 + i , 1 + 2i , 1 + 3i , .....

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3)

f(z) = z^2 - c , c = i & z_0 = i

z_0 = i
z_1 = (i)^2 - i = (-1) - i = -1 - i
z_1 = (-1 - i)^2 - i = (1 + 2i + i^2) - i = 1 + 2i - 1 - i = i
z_2 = (i)^2 - i = -1 - i

i , -1 - i , i , -1 - i , ......

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assuming you mean as n----> ∞

lim (4n^3 + 7n^2) / (5n^3 - 7n^2 + 3) =====> large in charge
n---> ∞

lim (4n^3) / (5n^3)
n---> ∞

lim (4/5) = 4/5
n---> ∞

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6)

(3x + y)^7
(3x + y)^2 * (3x + y)^2 * (3x + y)^2 * (3x + y)
(9x^2 + 6xy + y^2) * (9x^2 + 6xy + y^2) * (9x^2 + 6xy + y^2) * (3x + y)
(81x^4 + 108x^3y + 54x^2y^2 + 12xy^3 + y^4) * (9x^2 + 6xy + y^2) * (3x + y)
(729x^6 + 1458x^5y + 1215x^4y^2 + 540x^3y^3 + 135x^2y^4 + 18xy^5 +y^6) * (3x + y)
(2187x^7 + 5103x^6y + 5103x^5y^2 + 2835x^4y^3 + 945x^3y^4 + 189x^2y^5 + 21xy^6 +y^7

the fourth term is 2835x^4y^3 & 945x^3y^4

welcome welcome :)

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