Question 1

Multiply. Write the result in the form a + bi.
-(1 + 3i)(1 - 3i)

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 2

Multiply. Write the result in the form a + bi.
-(6 + 9i)(3 + 5i)

Accepted Answer

Use FOIL (first, outer, inner, last) method to multiply:
(6 + 9i)(3 + 5i) = 18 + 30i + 27i + 45i^2
Simplify by combining like terms and using i^2 = -1:
= (18 - 45) + (30 + 27)i
= -27 + 57i
Therefore, the correct answer is C. To multiply two complex numbers, we can use FOIL.

(6 + 9i)(3 + 5i) = 18 + 30i + 27i + 45i^2

Since i^2 = -1, we can simplify:

18 + 57i + 45(-1) = 18 + 57i - 45 = -27 + 57i

So the answer is (C).

Question 3

Multiply. Write the result in the form a + bi.
-

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 4

Divide.
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Accepted Answer

The answer of Divide.
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...

Question 5

Divide.
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Accepted Answer

To divide a hexadecimal number by 2, we can simply divide the last digit by 2. If the last digit is odd, we subtract 1 from it and add 8 to the next digit on the left. Therefore, the correct answer is obtained by dividing the last digit of the given hexadecimal number, which is 9, by 2 to get 4, and then subtracting 1 from the digit on the left, which is 1, and adding 8 to get c. Hence, the correct answer is B. To divide by 2 in hexadecimal, we only need to check if the last digit is even or odd. If it's even, we simply remove it. If it's odd, we subtract 1 from it before removing it and add 8 to the next digit. Following this rule, we get:

11ebb63d_1c06_ccfe_b851_77b6db7d2c89 / 2 = 11ebb63d_1c06_ccfe_b851_77b6db7d2c8  (odd digit 9 becomes 8 and 2 in the next digit becomes A)

The only choice that matches this result is B.

Question 6

Multiply. Write the result in the form a + bi.
-

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 7

Multiply. Write the result in the form a + bi.
-(7 + 5i)(4 - 3i)

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 8

Multiply. Write the result in the form a + bi.
-3i(7 - 2i)

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 9

Multiply. Write the result in the form a + bi.
-

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 10

Divide.
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Accepted Answer

When dividing by 2, the last digit of the hexadecimal number will be divided by 2 (in this case, 3 divided by 2 is 1 with a remainder of 1). Therefore, the new last digit will be 1. Taking this into consideration, the only option that has a 1 in the correct position is option A. The division should be done by subtracting the digits of the second number from the digits of the first number, from left to right. In this case, the sixth digit of the first number (3) is not enough to subtract from the second number (7), so we need to borrow 1 from the fifth digit of the first number, making it 6. Then we can subtract 7 from 16, getting 9. The rest of the digits can be subtracted normally. Therefore, the answer is 11ebb63d_1c06_7ed4_b851_553c4773a3de_TB8475_11.

Question 11

Multiply. Write the result in the form a + bi.
-

Accepted Answer

Since we are given no context about what numbers we are multiplying, it is impossible to know the actual value of the product. However, the format of the answer is always a + bi, where a and b are real numbers. The only choice that follows this format is B, so it must be the correct answer. It is impossible to determine the numerical values of the factors from the given information, as they are represented in hexadecimal format. However, based on the given options, option B is the only one with a different last digit (2da vs. 57fd), indicating that it may be the product of the other two factors. To confirm this, we would need to convert all numbers to decimal format and perform the multiplication.

Question 12

Add or subtract.
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Accepted Answer

The answer of Add or subtract.
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Question 13

Add or subtract.
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Accepted Answer

To add or subtract hexadecimal numbers, we simply do the same as we do with decimal numbers. We add or subtract digits in the same positions. In this case, we need to add 2000 to the second group of digits (9450 + 2000 = bb50) to get the answer in choice A. The other choices have incorrect digits in the fourth group. To add or subtract hexadecimal numbers, we must align them and perform the operation on each corresponding digit. In this case, we need to change the third digit from 5 to b (as b-5=6). Hence, the correct answer is A.

Question 14

Divide.
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Accepted Answer

The answer of Divide.
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...

Question 15

Multiply. Write the result in the form a + bi.
- i

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 16

Add or subtract.
-(8 - 2i) + (-8 + 2i)

Accepted Answer

When we add (8 - 2i) and (-8 + 2i), we get:

(8 - 2i) + (-8 + 2i) = 8 + (-8) + (-2i + 2i) = 0

Therefore, the answer is D. When we add (8-2i) and (-8+2i), we get 0. Therefore, the answer is D.

Question 17

Divide.
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Accepted Answer

The answer of Divide.
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...

Question 18

Multiply. Write the result in the form a + bi.
-

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 19

Multiply. Write the result in the form a + bi.
-(6 - 6i)(6 + 8i)

Accepted Answer

The answer of Multiply. Write the result in the form...

Question 20

Add or subtract.
-

Accepted Answer

The answer of Add or subtract.
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...

Quiz 11: Roots, Radicals, and Complex Numbers

Multiply. Write the result in the form a + bi. -(1 + 3i) (1 - 3i)

Multiply. Write the result in the form a + bi. -(6 + 9i) (3 + 5i)

Multiply. Write the result in the form a + bi. -

Divide. -

Divide. -

Multiply. Write the result in the form a + bi. -

Multiply. Write the result in the form a + bi. -(7 + 5i) (4 - 3i)

Multiply. Write the result in the form a + bi. -3i(7 - 2i)

Multiply. Write the result in the form a + bi. -

Divide. -

Multiply. Write the result in the form a + bi. -

Add or subtract. -

Add or subtract. -

Divide. -

Multiply. Write the result in the form a + bi. - i

Add or subtract. -(8 - 2i) + (-8 + 2i)

Divide. -

Multiply. Write the result in the form a + bi. -

Multiply. Write the result in the form a + bi. -(6 - 6i) (6 + 8i)

Add or subtract. -