Question

If x = (10 − 3i) and y = (3 − 10i), then xy = -109i and x/y =

Answer 1

Xy = -109i
We could find the value of i by substitute the algebraic form of x and y to the equation above

xy = -109i
(10 - 3i)(3 - 10i) = -109i
(10)(3) -3i(3) + 10(-10i) - 3i(-10i) = -109i
30 - 9i - 100i -30i² = -109i

multiply both side by -1
-30 + 9i + 100i + 30i² = 109i
30i² + 9i + 100i - 109i - 30 = 0
30i² - 30 = 0
30i² = 30
i² = 1
i = -1 or i = 1

Then find the value of x and y if i = -1
If i = -1, therefore
x = 10 - 3(-1)
x = 10 + 3
x = 13

y = (3 - 10i)
y = 3 - 10(-1)
y = 3 + 10
y = 13

x/y = 13/13 = 1

Then find the value of x and y if i = 1
x = 10 - 3(1)
x = 10 - 3
x = 7

y = (3 - 10i)
y = 3 - 10(1)
y = 3 - 10
y = -7

x/y = 7/-7 = -1

The value of x/y is either 1 or -1

Answer 2

Answer:

x/y is either 1 or -1.

Step-by-step explanation:

Given :  x = (10 − 3i) and y = (3 − 10i), Then xy = -109 i

To find  : x/y

Solution : We have x = (10 − 3i) and y = (3 − 10i),

We need to find x/y

Given xy = -109i

(10 - 3i)(3 - 10i) = -109i .

Distributes 10 over (3 -10i) and -3i over (3 -10i).

(10)(3) -3i(3) + 10(-10i) - 3i(-10i) = -109i

30 - 9i - 100i -30i² = -109i

multiply both side by -1

-30 + 9i + 100i + 30i² = 109i

30i² + 9i + 100i - 109i - 30 = 0

30i² - 30 = 0

30i² = 30

i² = 1

Taking square root both sides

i = -1 or i = 1

Then find the value of x and y if i = -1

If i = -1, therefore

x = 10 - 3(-1)

x = 10 + 3

x = 13

y = (3 - 10i)

y = 3 - 10(-1)

y = 3 + 10

y = 13

x/y = 13/13 = 1

Then find the value of x and y if i = 1

x = 10 - 3(1)

x = 10 - 3

x = 7

y = (3 - 10i)

y = 3 - 10(1)

y = 3 - 10

y = -7

x/y = 7/-7 = -1

The value of x/y is either 1 or -1

Therefore,  x/y is either 1 or -1.