1. What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers? A. a complex number
B. a real number
C. an imaginary unit
D. a pure imaginary number

2. Which of the following statements is not true?
A. In order for a+bi to be a complex number, b must be nonzero.
B. A complex number is a number that can be written in the form a+bi where a and b are real numbers.
C. For a complex number written in the form a+bi, the value of a is called the real part of the complex number.
D. Every real number is also a complex number.

3. What is the real part of 4−5i?

4. What is the imaginary part of 7−6i?

5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting −10−−−−√ in terms of i results in −10i.
A. This statement is true.
B. This statement is false. Rewriting −10−−−−√ in terms of i results in 10i.
C. This statement is false. Rewriting −10−−−−√ in terms of i results in −10−−−−√i.
D. This statement is false. Rewriting −10−−−−√ in terms of i results in 10−−√i.

Re-writing question 5:

5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting √-10 in terms of i results in −10i.

A. This statement is true.

B. This statement is false. Rewriting √-10 in terms of i results in (√10)i.

C. This statement is false. Rewriting √-10 in terms of i results in −10√i.

D. This statement is false. Rewriting √-10 in terms of i results in 10√i.

1) C. an imaginary number

2) A. In order for a + bi to be a complex number, b must be nonzero

3) 4

4) -6

5) B. The statement is false. Rewriting √-10 in terms of i results in (√10)i

Step-by-step explanation:

1. When a number can be expressed in the form a+bi where a and b are real numbers, then the number is said to be a complex number.

For example, the following are complex numbers where i = √-1 ;

i. 3 + 5i

ii. 4 - 7i

iii. -3 - 9i

Well, even real numbers are a subset of complex numbers. For example,

=> 5 can be written as 5 + 0i

=> -12 can be written as -12 + 0i

-- But when a and b are non-zero real numbers or at least b is a non-zero real number, then the number is said to be an imaginary number.

-- If a is zero, then the number is a purely imaginary number

-- If b is zero, then the number is a purely real number

2. For a number to be called a complex number;

i. it can be written in the form a + bi where a and b are real numbers,

ii. either a or b, or both, may be zero,

iii. a is the real part of the complex number,

iv. b is the imaginary part of the complex number.

v. it could also be a real number since every real number is also a complex number.

3. Given 4 - 5i

The real part is 4

and the imaginary part is -5

4. Given 7 - 6i

The real part is 7

and the imaginary part is -6

5. Rewrite √-10 in terms of i

Remember that i = √-1

Therefore,

√-10 = √(-1 x 10) = √-1 x √10

=> √-10 = √-1 x √10

=> √-10 = i x √10

=> √-10  = (√10)i

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