SAT Practice Test - Math - Complex Numbers

SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving questions that focus on Complex Numbers.

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SAT Practice Test 2015. Which of the following complex numbers is equivalent to $\frac{3-5i}{8+2i}$? (Note: $i=\sqrt{-1}$)

A) $\frac{3}{8}-\frac{5i}{2}$

B) $\frac{3}{8}+\frac{5i}{2}$

C) $\frac{7}{34}-\frac{23i}{34}$

D) $\frac{7}{34}+\frac{23i}{34}$

Answer:

$\frac{3-5i}{8+2i}=$

$\frac{3-5i}{8+2i}*\frac{8-2i}{8-2i}=$

$\frac{24-6i-40i-10}{64+4}=$

$\frac{14-46i}{68}=$

$\frac{7-23i}{34}$

Answer: C

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SAT Test 2015. For $i=\sqrt{-1}$ , what is the sum $(7+3i)+(-8+9i)$?
A) -1+12i
B) -1-6i
C) 15+12i
D) 15-6i

Answer:

$(7+3i)+(-8+9i)=$
$7-8+3i+9i=$
$-1+12i$

Answer: A

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SAT Practice Test. Which of the following is equal to $(14-2i)(7+12i)$? (Note: $i=\sqrt{-1}$.)
A. 74
B. 122
C. 78+154i
D. 122+154 i

Answer:

$(14-2i)(7+12i)=$
$14.7+14.12i-2i.7-2i.12i=$
$98+168i-14i-24.i^2=$
$98+154i-24.(-1)=$
$98+154i+24=$
$122+154i$

Answer: D

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