Applying properties of operations on complex numbers to solve problems

Solve the equation (2 + 3i)x = (4 - 5i) for x.

• x = (4 + 5i) / (2 + 3i)

• x = (4 - 5i) / (2 - 3i)

• x = (4 - 5i) / (2 + 3i)

• x = (4 + 5i) / (2 - 3i)

Calculate the product of (1 + 4i) and (2 - 3i).

• 10 - 12i

• 14 + 5i

• 6 + 7i

• 3 + 2i

• A

• B

• C

• D

The product of (3 -2i) and (7+6i) is

• 21 - 12i
• 9 + 4i
• 33 + 4i
• 21 + 16i

Let w₁= 4 - 2i, w₂ = -3 + 4i, and w₃= 2 + 6i. Which of the following is equal to w₁w₂ - w₃ ?

• -2 + 28i

• -4 + 22i

• -6 +28i

• -6 + 16i

• -2 +16i

 $\left(-6i\right)\left(-6-2i\right)+\left(3i\right)\left(8+4i\right)$  

•  $-24+75i$  
  

•  $-12+72i$  
  

•  $12i$  
  

•  $-24+60i$  

What is the product of (2 + 3i) and (4 - 5i)?

• Charlotte thinks it's -23 + 2i

• Mia thinks it's 23 + 2i

• Evelyn thinks it's -23 - 2i

• No one thinks it's 23 - 2i

Calculate the product of (-2 + 3i) and (-1 - 4i).

• -14 - 5i

• 14 - 5i

• 14 + 5i

• -14 + 5i

(3 - 2i)*(5 + 4i) - (3+2i)*(5+4i)

• -16 - 20i

• 16 - 20i

• 0

• 30 + 24i

• non of the above