Question

Drag the tiles to the correct boxes to complete the pairs

Answer 1

$\begin{gathered} -5x+y=\rightarrow-8-41i \\ x\cdot2y=\rightarrow58+106i \\ -x\cdot y=\rightarrow-29-53i \\ 2x-3y=\rightarrow-15+19i \end{gathered}$

Explanation

Let

$\begin{gathered} x=3+8i \\ y=7-i \end{gathered}$

now, to multiply a imaginary number, multiply the constant

and when adding or subtracting another number, just ad/sub component to component

so

Step 1

a)-5x+y

$\begin{gathered} -5x+y \\ replace \\ -5(3+8i)+(7-i)=\mleft(-15-40i\mright)+\mleft(7-i\mright) \\ -5x+y=(-15+7)+(-40i-i) \\ -5x+y=-8-41i \end{gathered}$

Step 2

b)x*2y

$\begin{gathered} x\cdot2y=(3+8i)\cdot2(7-i) \\ x\cdot2y=(3+8i)\cdot(14-2i) \\ x\cdot2y=(3\cdot14)+(3)(-2i)+(8i)(14)+(8i)(-2i) \\ x\cdot2y=42-6i+112i-16(i^2) \\ x\cdot2y=42-6i+112i-16(-1) \\ x\cdot2y=42-6i+112i+16 \\ \text{add like terms} \\ x\cdot2y=58+106i \\ \end{gathered}$

Step 3

c)-x*y

$\begin{gathered} -x\cdot y=-(3+8i)\cdot(7-i) \\ -x\cdot y=(-3-8i)\cdot(7-i) \\ -x\cdot y=(-3)(7)+(-3)(-i)-(8i)(7)+(8i)(i) \\ -x\cdot y=-21+3i-56i+8(i^2) \\ -x\cdot y=-21+3i-56i+8(-1) \\ -x\cdot y=-21-53i-8 \\ -x\cdot y=-29-53i \end{gathered}$

Step 4

d)2x-3y

$\begin{gathered} 2x-3y= \\ 2x-3y=2(3+8i)-3(7-i) \\ 2x-3y=6+16i-21+3i \\ 2x-3y=-15+19i \end{gathered}$

I hope this helps you