Applying Properties of Operations on Complex Numbers to Solve Problems

If z=√2+√2 i then arg(z²)=

• 0^o

• 60^o

• 90^o

• Not Possible

• A

• B

• C

• D

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

• -16 - 20i

• 16 - 20i

• 0

• 30 + 24i

• non of the above

The complex numbers u and v satisfy the equations u + 2v = 2i and iu + v = 3. Solve the equations for u and v, giving both answers in the form x + iy, where x and y are real.

• u = -2 - 2i

  v = 1 + 2i

• u = 2 + 2i

  v = 1 - 2i

• u = 2i - 2

  v = -1 - 2i

• u = 1 + 2i

  v = - (2 + 2i)

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)

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

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