Answer:
A. [tex]\sqrt{-64}[/tex] = 8i
B. 8i + 5i = 13i
C. Â 8i - 5i = 3i
D. 8i x 5i = -40
Step-by-step explanation:
A. The square root of any negative number would lead to a complex number. Complex numbers are number which consist a complex part denoted by i.
-1 = [tex]i^{2}[/tex]
[tex]\sqrt{-1}[/tex] = [tex]\sqrt{i^{2} }[/tex] = i
Example: 1. What is the square root of -64?
square root of -64 = [tex]\sqrt{-64}[/tex]
             = [tex]\sqrt{-1 *64}[/tex]
             = [tex]\sqrt{-1}[/tex] x [tex]\sqrt{64}[/tex]
             = i x 8
             = 8i
[tex]\sqrt{-64}[/tex] = 8i
2. find the square root of -25.
[tex]\sqrt{-25}[/tex] = [tex]\sqrt{-1*25}[/tex]
     = 5i
B. To add two complex numbers, they are considered as algebraic expressions.
Example, the sum of 8i and 5i can be determined as;
         8i + 5i = 13i
C. To add two complex numbers, they are considered as algebraic expressions.
Example, the subtraction of 8i and 5i can be determined as;
         8i - 5i = 3i
D. To multiply two complex numbers, the complex part is considered.
Example, determine the product of 8i and 5i.
8i x 5i = 8 x 5 x i x i
     = 40[tex]i^{2}[/tex]
     = -40         (∵    [tex]i^{2}[/tex] = -1)
8i x 5i = -40
