98 points : ) 1 which of the following is the conjugate of a complex number with 5 as the real part and −2i as the imaginary part? 5 + 2i −5 − 2i −5 + 2i 5 − 2i 2 simplify the expression the root of negative nine over the quantity of three minus two i plus the quantity of one plus five i.. the quantity of twelve minus nine i all over twenty five. the quantity of twelve minus nine i all over seven. the quantity of nine plus twelve i all over twenty five. the quantity of nine plus twelve i all over seven. 3 simplify 4 times square root 24 minus 4 square root 8 plus square root of 98. 7 square root 2 23 square root 2 negative square root 2 plus 16 square root 3 negative square root 2 plus 8 square root 6 4 simplify 3 times the 3rd root of 16. 5 times the 3rd root of 2 6 times the 3rd root of 2 12 times the 3rd root of 2 27 times the 3rd root of 2 5 use the table below to answer this question: x y −1 −3 0 −1 2 3 find the average rate of change for the given function from x = −1 to x = 2. −2 −1 1 2

1. Concept: Complex numbers of the form (a+bi) and (a-bi) which have the same real parts and whose imaginary parts differ in sign only, are called conjugate of each other.

Correction: 5 is a real part and -2i is an imaginary number(not imaginary part) (but -2 is known as imaginary part :)

in this question,

z= 5-2i

z* = 5+2i ( conjugate of z with real part as it is and imaginary part(opposite in sign))

A is the correct answer.

2.

first simplify the denominator which is √-9 = √9 *√-1 = 3*i = 3i

now simplify the denominator which is 3-2i+(1+5i) = 4+3i

now multiply and divide it by (4-3i)(which is the conjugate of 4+3i)

⇒ i² = -1 so

C is the correct answer.

3. 4√24 -4√8 +√98

you can write 24 as 6*4, 8 as 4*2, 98 as 49*2.

= 4√(6*4) -4√(4*2) +√(49*2)

= 4*√6 *√4 -4*√4 *√2 +√49* √2

= 4*2*√6 -4*2 *√2 + 7* √2

= 8√6 -8√2 +7√2

= 8√6 +√2(-8+7)

= 8√6 -√2

D is the correct answer.

4. 3∛16

you can write 16 as 2*2³ and ∛ as .

=

= *

= 3* 2 * ∛2

= 6∛2

B is the correct answer.

5. The average rate of change for a given function from x=-1 to x=2 = Δy/Δx

so,

Δy/Δx = (-1-(-3))/ (0-(-1))

Δy/Δx = (-1+3)/ (0+1)

Δy/Δx = 2/ 1

average rate of change of given function=Δy/Δx = 2

D is the correct answer.