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.
Answer:
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
