Question

Consider the imaginary numbers.

(a) what makes the following an imaginary number? (Use complete sentences)

Answer 1

Hello from MrBillDoesMath!

Answer:

See Discussion below

Discussion:

a) The sqrt( -50) is an imaginary number because -50 is < 0.

(By way of contrast: sqrt(50) is a real number)

b. sqrt(-50)/ sqrt(5) =

sqrt ( 25 * 2 * (-1)) / sqrt (5) =

5 sqrt(2) * i / sqrt(5) = (as sqrt(25) = 5 and 5 = sqrt(5) * sqrt(5) )

sqrt(5) * sqrt(2) * i =

sqrt(10) *i

c. i^22 =

(i^2)^10 * i^2 =

(-1)^10 * (-1) = => as (-1)^10 = +1

=-1

Thank you,

MrB