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Question

1. Perform the following complex number multiplication and write the answer in standard form

(-1+5i)(-3-5i)

2. Scott drove 220 miles using 8 gallons of gas. At the same rate, how many gallons of gas does he need for a trip of 308 miles?

3. Simplify the complex number as much as possible

i^31

Thank you

Answer 1

FOIL

(- 1 + 5i)(- 3 - 5i) =

3 - 15I + 5I - 25I² =

3 - 10I - 25(- 1) =

3 - 10I + 25 =

28 - 10I

- - - - - - - - -s-

Answer 2

(-1 + 5i) (-3 - 5i) = +3 + 5i -15i -25i^2 = 3 -10i -25i^2 = 3 -10i + 25 (remember that i^2 is -1 and -25 multiplied by -1 gives +25)

= 28 -10i

2. 220 miles is to 8 gallons as 308 miles is to x gallons

220/8 = 308/x or x = 308 X 8/220 = 2464/220 = 11.2 gallons

3. i^31 = i^30.i = -i (remember that i^2, i^4 etc. are all equal to -1. All odd powers of i will be equal to -i and all even powers of i will be equal to -1.)

Answer 3

Answer 1 is correct for problem 1.

For problem 2. First divide 220 miles by 8 gallons. This gives you 27.5 miles per gallon. Now, divide the 308 miles by this rate. 308/27.5 = 11.2. Using the factor label method, miles cancel out and you are left with gallons. So it takes 11.2 gallons to drive 308 miles.

For problem 3. i^2 = -1 Then i^4 = i^2 * i^2 = -1 * -1 = 1. So,
every even exponent not divisible by 4 will be -1 and every exponent divisible by 4 will be 1. We can write i^31 as i^30 * i. 30 is not divisible by 4 so this is -1 * i or -i.

Answer 4

(-1+5i)(-3-5i) = 3 + 5i -15i +25 = 28 - 10i.

no of gallons = 308/220 * 8 = 11.2 gallons.

Answer 5

2. 8 / 220 gallons for a mile, so (8 / 220) x 308 = 11.2 gallons for 308 miles

3. -i

Answer 6

1. FOIL

3 + 5i - 15i - 25i^2 = 3 - 10i + 25 = 28 - 10i

Answer 7

2. (8*308):220=?