Question

Let i be the imaginary number −1− root. Determine whether the expression a+bi, where a and b are real numbers, represents a real number or a non-real complex number for each case below. Select Real Number or Non-Real Complex Number for each case.

a. a=3, b=0
b. a=0, b=−5
c. a=−2, b=4

Answer 1

The number a+bi is considered a real number if b=0, and a non-real complex number if b is not zero. For a=3, b=0 it is a real number; for a=0, b=-5 and a=-2, b=4, both are non-real complex numbers.

Step-by-step explanation:

When considering whether an expression a+bi, where a and b are real numbers, represents a real number or a non-real complex number, we follow the definition of the imaginary unit i which is ∑-1.

• For case (a) a=3, b=0, we have an expression of 3+0i, which is a Real Number.
• For case (b) a=0, b=-5, the expression becomes 0-5i which is a Non-Real Complex Number.
• In case (c) a=-2, b=4 the expression -2+4i again represents a Non-Real Complex Number.

The imaginary part b determines the nature of the number. If b is zero, the number is real. If b is non-zero, it is a complex number.