Simplify the expression (4 + 5i)(4 − 5i). 16 − 20i 16 + 20i −9 41

41

Step-by-step explanation:

Simplify the following:

(5 i + 4) (-5 i + 4)

Hint: | Multiply 4 + 5 i and 4 - 5 i together using FOIL.

(4 + 5 i) (4 - 5 i) = (4) (4) + (4) (-5 i) + (5 i) (4) + (5 i) (-5 i):

4×4 + 4 (-5 i) + 5 i×4 + 5 i (-5 i)

Hint: | Multiply 4 and 4 together.

4×4 = 16:

16 - 5×4 i + 5 i×4 + 5 i (-5)×i

Hint: | Multiply 4 and -5 together.

4 (-5) = -20:

16 + -20 i + 5 i×4 + 5 i (-5)×i

Hint: | Multiply 5 and 4 together.

5×4 = 20:

16 - 20 i + 20 i + 5 i (-5)×i

Hint: | Combine products of like terms.

5 i (-5)×i = 5 i^2 (-5):

16 - 20 i + 20 i + -5×5 i^2

Hint: | Evaluate i^2.

i^2 = -1:

16 - 20 i + 20 i - 5×5×-1

Hint: | Multiply 5 and -1 together.

5 (-1) = -5:

16 - 20 i + 20 i - 5-5

Hint: | Multiply -5 and -5 together.

-5 (-5) = 25:

16 - 20 i + 20 i + 25

Hint: | Evaluate 16 - 20 i + 20 i + 25.

16 - 20 i + 20 i + 25 = 41:

 41

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: