Question

drag the tiles to the correct boxes to complete the pairs. given that x = 4 + 5i and y = 2 - 9i, match the equivalent expressions. 106 - 52i 14 + 29i 2 - 32i 53 - 26i x·y -x + 3y 2x·y 4x - y

Explanation:

Step1: Calculate $x \cdot y$

Use FOIL method for complex numbers:

$$\begin{align*} x \cdot y&=(4+5i)(2-9i)\\ &=4\cdot2 + 4\cdot(-9i) + 5i\cdot2 + 5i\cdot(-9i)\\ &=8 - 36i + 10i - 45i^2\\ &=8 - 26i - 45(-1)\\ &=8 - 26i + 45\\ &=53 - 26i \end{align*}$$

Step2: Calculate $-x + 3y$

Substitute $x,y$ and simplify:

$$\begin{align*} -x + 3y&=-(4+5i)+3(2-9i)\\ &=-4 -5i +6 -27i\\ &=(-4+6)+(-5i-27i)\\ &=2 - 32i \end{align*}$$

Step3: Calculate $2x \cdot y$

Use result of $x\cdot y$:

$$\begin{align*} 2x \cdot y&=2(x \cdot y)\\ &=2(53 - 26i)\\ &=106 - 52i \end{align*}$$

Step4: Calculate $4x - y$

Substitute $x,y$ and simplify:

$$\begin{align*} 4x - y&=4(4+5i)-(2-9i)\\ &=16 +20i -2 +9i\\ &=(16-2)+(20i+9i)\\ &=14 + 29i \end{align*}$$

Answer:

$x \cdot y
ightarrow 53 - 26i$
$-x + 3y
ightarrow 2 - 32i$
$2x \cdot y
ightarrow 106 - 52i$
$4x - y
ightarrow 14 + 29i$