Real and Complex Numbers

Practice Questions

SAT Subject Test in Math II › Real and Complex Numbers

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1

Let be a complex number. $\overline{x}$ denotes the complex conjugate of .

$x+\overline{ x} = 20$ and $x \overline{ x} = 200$ .

How many of the following expressions could be equal to ?

(a)

(b)

(c)

(d)

2

Multiply: $\left ( 4+ 7i\right )(4 - 7i)$

3

Evaluate:

$\left ( 7+3i\right )^{2}$

4

The fraction $\frac{5+3i}{2-2i}$ is equivalent to which of the following?

5

$\overline{x}$ denotes the complex conjugate of .

If $x = \frac{1}{10} - \frac{1}{5} i$ , then evaluate $\overline{x}^{2} - x^{2}$ .

6

is a complex number; $\overline{x}$ denotes the complex conjugate of .

$x \cdot \overline{x} = 84$

Which of the following could be the value of ?

7

Multiply:

$-3 i \cdot 8i \cdot 5i \cdot 6i$

8

Which of the following is equal to $i^{77}$ ?

9

Which of the following is equal to $\left ( 4i\right )^{4}$ ?

10

Evaluate:

$(6 +5i)^{2}$

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