Write as a Vector Equality

Problem

x=−3−2*i,y=x*(x+2)*(x+6)*(x+3−2*i)*(x+9+6*i)*(x+9−6*i)

Solution

1. Substitute the value of x into the expression for y to evaluate each factor individually.

2. Evaluate the first three factors:

x=−3−2*i

x+2=(−3−2*i)+2=−1−2*i

x+6=(−3−2*i)+6=3−2*i

3. Evaluate the remaining three factors:

x+3−2*i=(−3−2*i)+3−2*i=−4*i

x+9+6*i=(−3−2*i)+9+6*i=6+4*i

x+9−6*i=(−3−2*i)+9−6*i=6−8*i

4. Multiply the factors together to find the value of y

y=(−3−2*i)*(−1−2*i)*(3−2*i)*(−4*i)*(6+4*i)*(6−8*i)

(−3−2*i)*(−1−2*i)=3+6*i+2*i−4=−1+8*i

(−1+8*i)*(3−2*i)=−3+2*i+24*i+16=13+26*i

(13+26*i)*(−4*i)=−52*i+104=104−52*i

(104−52*i)*(6+4*i)=624+416*i−312*i+208=832+104*i

(832+104*i)*(6−8*i)=4992−6656*i+624*i+832=5824−6032*i

5. Express the complex numbers x and y as vectors in the form ([Re],[Im])

Final Answer

([x],[y])=([−3−2*i],[5824−6032*i])

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