500 Review Questions and Answers
The commutative law allows us to rewrite this as
ja+jb=j(b+a)
and the distributive law, applied again, gives us
ja+jb=jb+ja
Question 21-6
What is the absolute value of j25? What is the absolute value of −j25?
Answer 21-6
Remember that in general, if b is any nonnegative real number, then
|jb|=b
and
|−jb|=b
The absolute value of j25 and the absolute value of −j25 are therefore both equal to 25.
Question 21-7
How is a complex number “put together”?
Answer 21-7
A complex number is the sum of a real number and an imaginary number. If we have two real
numbersa and b, then a+jb is a complex number. Conversely, any complex number can be
written in the form a+jb, where a and b are real numbers. There are no restrictions on the
values of a or b. They can be negative, positive, or 0.
Question 21-8
What is the sum of the complex numbers a 1 +jb 1 and a 2 +jb 2 , where a 1 ,a 2 ,b 1 , and b 2 are real
numbers?
Answer 21-8
When we want to add two complex numbers, we add the real parts and the complex parts
separately. Therefore,
(a 1 +jb 1 )+ (a 2 +jb 2 )= (a 1 +a 2 )+ (jb 1 +jb 2 )
= (a 1 +a 2 )+j(b 1 +b 2 )
Question 21-9
What is the product of the complex numbers a 1 +jb 1 and a 2 +jb 2 , where a 1 ,a 2 ,b 1 , and b 2 are
real numbers?