Solve (3+2yi)(4+i)-(3+2yi)(6+i)

$$( 3 + 2 y i ) ( 4 + i ) - ( 3 + 2 y i ) ( 6 + i )$$

Evaluate

$$-4iy-6$$

Solution Steps

Multiply 2 and i to get 2i.

$$\left(3+2iy\right)\left(4+i\right)-\left(3+2yi\right)\left(6+i\right)$$

Use the distributive property to multiply 3+2iy by 4+i.

$$12+3i+\left(-2+8i\right)y-\left(3+2yi\right)\left(6+i\right)$$

Multiply 2 and i to get 2i.

$$12+3i+\left(-2+8i\right)y-\left(3+2iy\right)\left(6+i\right)$$

Use the distributive property to multiply 3+2iy by 6+i.

$$12+3i+\left(-2+8i\right)y-\left(18+3i+\left(-2+12i\right)y\right)$$

To find the opposite of 18+3i+\left(-2+12i\right)y, find the opposite of each term.

$$12+3i+\left(-2+8i\right)y+\left(-18-3i\right)+\left(2-12i\right)y$$

Combine the real and imaginary parts.

$$\left(-2+8i\right)y+\left(2-12i\right)y+12-18+\left(3-3\right)i$$

Do the additions.

$$\left(-2+8i\right)y+\left(2-12i\right)y-6$$

Combine \left(-2+8i\right)y and \left(2-12i\right)y to get -4iy.

$$-4iy-6$$

Expand

$$-4iy-6$$

Solution Steps

Multiply 2 and i to get 2i.

$$\left(3+2iy\right)\left(4+i\right)-\left(3+2yi\right)\left(6+i\right)$$

Use the distributive property to multiply 3+2iy by 4+i.

$$12+3i+\left(-2+8i\right)y-\left(3+2yi\right)\left(6+i\right)$$

Multiply 2 and i to get 2i.

$$12+3i+\left(-2+8i\right)y-\left(3+2iy\right)\left(6+i\right)$$

Use the distributive property to multiply 3+2iy by 6+i.

$$12+3i+\left(-2+8i\right)y-\left(18+3i+\left(-2+12i\right)y\right)$$

To find the opposite of 18+3i+\left(-2+12i\right)y, find the opposite of each term.

$$12+3i+\left(-2+8i\right)y+\left(-18-3i\right)+\left(2-12i\right)y$$

Combine the real and imaginary parts.

$$\left(-2+8i\right)y+\left(2-12i\right)y+12-18+\left(3-3\right)i$$

Do the additions.

$$\left(-2+8i\right)y+\left(2-12i\right)y-6$$

Combine \left(-2+8i\right)y and \left(2-12i\right)y to get -4iy.

$$-4iy-6$$