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**Aileys.** Would some kind soul with access to this book pretty please post the following questions for me? I need to do these for my class and all the copies in the library are gone & all the ones from the bookshop sold out!

Section 1.3: questions 14 & 16

14) Show that a correct formula for $\displaystyle \arg(x+iy)$ can be computed using the form

$\displaystyle \arg(x+iy)=\left\{\begin{array}{ll}\arctan(y/x)+\frac{\pi}{2}[1-sgn(x)]&\,if\,\,x\neq 0\\\frac{\pi}{2}sgn(y)&\,if\,\,x=0\,,\,y\neq 0\\unde{f}ined &\,if\,\,x=y=0\end{array}\right.$

with $\displaystyle sgn(t)=\left\{\begin{array}{rl}1&\,if\,\,t>0\\0&\, if\,\,t=0\\-1&\,if\,\,t<0\end{array}\right.$

Show also that the expression $\displaystyle sgn(y)\arccos \frac{x}{\sqrt{x^2+y^2}}$ , at its points of continuity, equals $\displaystyle \arg(x+iy)$

16) Prove that $\displaystyle ||z_1|-|z_2||\leq |z_1-z_2|$

Section 1.5: question 5 parts d & f, question 8, question 10

5) Find the values of (d) $\displaystyle (1-\sqrt{3}i)^{1/3}$ ; (f) $\displaystyle \left(\frac{2i}{1+i}\right)^{1/6}$

8) Let $\displaystyle a,b,c\in\mathbb{R}\,,\,a\neq 0$ . Show that the equation $\displaystyle az^2+bz+c=0$ has (a)two real solutions if $\displaystyle b^2-4ac>0$ , (b) two non-real conjugate solutions if $\displaystyle b^2-4ac <0$

10) Find all four roots of the equation $\displaystyle z^4+1=0$ and use them to deduce the factorization $\displaystyle z^4+1=(z^2-\sqrt{2}z+1)(z^2+\sqrt{2}z+1)$

Section 1.6: questions 11 & 12

Section 2.1: question 2 parts c & d, question 3 parts b & d, question 4,question 10 parts b & d

Thanks so much to anyone that can help me out