Complex Numbers and Matrices

Answer explanation

To convert the complex number 5 + 12i to polar form, we find the modulus r = √(5² + 12²) = 13 and the angle θ = tan⁻¹(12/5). Thus, the correct choice is 13(\cos \theta + i\sin \theta) where θ = tan⁻¹(12/5).

Tags

CCSS.HSN.CN.B.4

Answer explanation

To convert -1 + √3i to polar form, we find the modulus r = √((-1)² + (√3)²) = 2 and the argument θ = arctan(√3/-1) = 2π/3. Thus, the polar form is 2(cos(2π/3) + i sin(2π/3)).

Tags

CCSS.HSN.CN.B.4

Answer explanation

To convert -3 - 3i to polar form, calculate the modulus: r = √((-3)² + (-3)²) = 3√2. The angle θ = arctan(y/x) = arctan(1) + π = 5π/4. Thus, the polar form is 3√2(cos(5π/4) + i sin(5π/4)).

Tags

CCSS.HSN.CN.B.4

find: B*A

• 47     30
  9     5

• 17     15
  42     35

• 10     25
  7     1

• not possible because rows do not match columns

Tags

CCSS.HSN.VM.C.8

Refer to the above image, what is the conjugate of the denominator?

• 8 + 6i

• 6 + 8i

• 6 - 8i

• -6 +8i

Tags

CCSS.HSN.CN.A.3

Find the product of the two matrices.

• undefined

• -3   16
  17   12
  8   -10

• 3   12 
  -15  -8
  -1   -3

Tags

CCSS.HSN.VM.C.8

find: B*A

• 47     30
  9     5

• 17     15
  42     35

• 10     25
  7     1

• not possible because rows do not match columns

Tags

CCSS.HSN.VM.C.8

Tags

CCSS.HSN.CN.B.4

Answer explanation

To add the matrices, sum corresponding elements: \begin{bmatrix} 2+6 & 3+7 \ 4+8 & 5+9 \end{bmatrix} = \begin{bmatrix} 8 & 10 \ 12 & 14 \end{bmatrix}. Thus, the correct answer is \begin{bmatrix} 8 & 10 \ 12 & 14 \end{bmatrix}.

Tags

CCSS.HSN.VM.C.8

Answer explanation

To add the matrices, sum corresponding elements: \(1+4=5\), \(0+5=5\), \(3+6=9\), \(2+7=9\). Thus, the result is \(\begin{bmatrix} 5 & 5 \ 9 & 9 \end{bmatrix}\), which matches the correct answer.

Tags

CCSS.HSN.VM.C.8