A: (x + 5i)^2
= (x + 5i)(x + 5i)
= (x)(x) + (x)(5i) + (5i)(x) + (5i)(5i)
= x^2 + 5ix + 5ix + 25i^2
= 25i^2 + 10ix + x^2
B: (x - 5i)^2
= (x + - 5i)(x + - 5i)
= (x)(x) + (x)(- 5i) + (- 5i)(x) + (- 5i)(- 5i)
= x^2 - 5ix - 5ix + 25i^2
= 25i^2 - 10ix + x^2
C: (x - 5i)(x + 5i)
= (x + - 5i)(x + 5i)
= (x)(x) + (x)(5i) + (- 5i)(x) + (- 5i)(5i)
= x^2 + 5ix - 5ix - 25i^2
= 25i^2 + x^2
D: (x + 10i)(x - 15i)
= (x + 10i)(x + - 15i)
= (x)(x) + (x)(- 15i) + (10i)(x) + (10i)(- 15i)
= x^2 - 15ix + 10ix - 150i^2
= - 150i^2 + 5ix + x^2
Hope that helps!!!
Answer:
36 <127
(36,127°)
36 [ cos (127) + i sin (127)]
Step-by-step explanation:
w1 = 2 < 95
w2 = 18 < 32
w1 * w2
We multiply the magnitude and add the angles
w1 * w2 = 2*18 < (95+32)
=36 < 127
36 [ cos (127) + i sin (127)]
Answer:
cousin: m-3
uncle: 5m
together: 6m-3
Step-by-step explanation:
if her cousin is 3 years younger, they would be m-3. since their uncle is her age times 5, he would be 5m. add those and you get 5m+m-3. combine the m's (and get 6m), then add the -3 to get 6m-3
Answer:
Part 1) 
Part 2) The equation satisfy the set of coordinates (see the explanation)
Step-by-step explanation:
step 1
Find the linear equation
The rule for the linear equation states that y is three more than twice x.
so
The variable y is equal to the number 2 multiplied by x plus the number 3
step 2
Prove that the equation satisfies the set of coordinates
substitute the value of x and the value of y in the linear equation and then compare the results
a) (-1, 1)
----> is true
so
The equation satisfy the ordered pair
b) (0, 3)
----> is true
so
The equation satisfy the ordered pair
c) (-1/3,7/3)
----> is true
so
The equation satisfy the ordered pair
therefore
The equation satisfy the set of coordinates
