# Test: Complex Numbers I - Ambitious

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Question 1:   Solve: $\left(7+5i\right)-\left(2+3i\right)$
$12+8i$
$7$
$5-2i$
$5+2i$
Question 2:   Solve: $\left(2+3i\right)\left(3+4i\right)$
$6-12i$
$-6+17i$
$4+17i$
$2-12i$
Question 3:   Simplify: ${i}^{13}$
$-1$
$-i$
$1$
$i$
Question 4:   Simplify: ${\left(3-4i\right)}^{2}$
$9-16i$
$25-24i$
$-7-24i$
$-i$
Question 5:   Simplify: (2 - 5i)(2 + 5i)
$4-25i$
$4+25i$
$29$
$-16$
Question 6:   Simplify: ${i}^{27}$
$-i$
$1$
$-1$
$i$
Question 7:   Simplify: $\frac{4-3i}{2}$
$2-\frac{3}{2}i$
$2-3i$
$1$
$2-2i$
Question 8:   Simplify: $\frac{8-5i}{7+4i}$
$\frac{36}{65}-1\frac{2}{65}i$
$\frac{17}{28}-2\frac{4}{67}i$
$1\frac{2}{7}+1\frac{1}{15}i$
$1\frac{1}{6}-1\frac{1}{32}i$
Question 9:   Simplify: $\frac{-2-3i}{4+5i}$
$\frac{2}{15}+\frac{1}{17}i$
$-\frac{23}{41}-\frac{2}{41}i$
$-\frac{7}{25}+\frac{2}{43}i$
$\frac{13}{67}+\frac{2}{35}i$
Question 10:   Simplify: $\frac{\left(1+2i\right)\left(3-5i\right)}{6-8i}$
$\frac{27}{43}-\frac{47i}{59}$
$1+\frac{12i}{49}$
$\frac{7}{10}+1\frac{1}{10}i$
$-\frac{33}{47}+\frac{45i}{57}$