The product of (3 + 2i) and a complex number is (17 + 7i).

75

step-by-step explanation:

( - 4 , -7 )

all the lines must parallel  

step-by-step explanation:

coordinates of c = ( - 1 , 2 )

3 units left = ( -4 , 2 )

9 units down = ( - 4 , 11 )

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

d .tv

step-by-step explanation:

the side tv is included in both triangles.   this means it corresponds to itself in the transformation.

this is justified by using the reflexive property, which states that anything is congruent to itself.