# Test: Complex Numbers II - Ambitious

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Question 1:   If $\left(x+y\right)+\left(x-y\right)=5+3i$, find $x$ and $y$
$x=2,y=0$
$x=3,y=2$
$x=4,y=1$
$x=5,y=3$
Question 2:   Express $z=6+8i$ in the polar form
$z=10\left(\mathrm{sin}53.13°+i\mathrm{cos}53.13°\right)$
$z=10\left(\mathrm{cos}53.13°+i\mathrm{sin}53.13°\right)$
$z=14\left(\mathrm{cos}36.87°+i\mathrm{sin}36.87°\right)$
$z=10\left(\mathrm{cos}36.87°+i\mathrm{sin}36.87°\right)$
Question 3:   Express $z=4+3i$ in the shortened polar form
$z=7\overline{)36.87°}$
$z=4\overline{)36.87°}$
$z=5\overline{)53.13°}$
$z=5\overline{)36.87°}$
Question 4:   Express $z=-4-5i$ in the shortened polar form
$z=6\overline{)231.34°}$
$z=9\overline{)51.34°}$
$z=\sqrt{41}\overline{)51.34°}$
$z=\sqrt{41}\overline{)231.34°}$
Question 5:   Express $3\left(\mathrm{cos}15°+i\mathrm{sin}15°\right)$ in the form $a+ib$
$3+i$
$2.898+0.777i$
$1.457-2.721i$
$0.551+0.289i$
Question 6:   Express $7\left(\mathrm{cos}32°+i\mathrm{sin}32°\right)$ in the form $a+ib$
$3.71+5.936i$
$5.936+7i$
$7+2.56i$
$5.936+3.71i$
Question 7:   Express $5\overline{)237°}$ in the form $a+ib$
$1.625+2.785i$
$-2.725-4.195i$
$1.575+3.642i$
$4.395-3.115i$
Question 8:   Change $3\overline{)60°}$ to the exponential form
$3{e}^{-\frac{\pi }{3}i}$
$3{e}^{\frac{\pi }{3}i}$
$3{e}^{\frac{\pi }{2}i}$
$6{e}^{\pi i}$
Question 9:   Change $12\overline{)210°}$ to the exponential form
$12{e}^{\frac{6}{7}\pi i}$
$6{e}^{\frac{5}{6}\pi i}$
$12{e}^{\frac{5}{6}\pi i}$
$12{e}^{\frac{7}{6}\pi i}$
Question 10:   Change $7\overline{)197.5°}$ to the exponential form
$6{e}^{\frac{19}{18}\pi i}$
$7{e}^{\frac{79}{72}\pi i}$
$12{e}^{1.2\pi i}$
$12{e}^{\frac{19}{18}\pi i}$