Algebra Know-It-ALL

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?