To simplify the expression (3-2i)(1-6i), we can use the distributive property or FOIL method:
(3-2i)(1-6i) = 3(1) + 3(-6i) - 2i(1) - 2i(-6i)
Simplifying further:
= 3 - 18i - 2i + 12i^2
Since i^2 = -1, we can substitute this value:
= 3 - 18i - 2i + 12(-1)
Simplifying further:
= 3 - 18i - 2i - 12
= -9 - 20i
So, (3-2i)(1-6i) simplifies to -9-20i.
Simplify (3-2i)(1-6i)
11 answers
Evaluate 5-3|3•(-6)|
First, we evaluate the absolute value: |3•(-6)| = |-18| = 18.
Then, we substitute this value into the expression: 5-3•18.
Next, we perform the multiplication: 3•18 = 54.
Substituting this value back into the expression: 5-54.
Finally, we compute the subtraction: 5-54 = -49.
Therefore, 5-3|3•(-6)| simplifies to -49.
Then, we substitute this value into the expression: 5-3•18.
Next, we perform the multiplication: 3•18 = 54.
Substituting this value back into the expression: 5-54.
Finally, we compute the subtraction: 5-54 = -49.
Therefore, 5-3|3•(-6)| simplifies to -49.
Solve 1/4-2/x=3/x
To solve the equation (1/4) - (2/x) = (3/x), we can first find a common denominator. The common denominator for the fractions is 4x.
Multiplying every term by 4x:
(4x)(1/4) - (4x)(2/x) = (4x)(3/x)
This simplifies to:
x - 8 = 12
Next, we isolate the variable x by adding 8 to both sides of the equation:
x - 8 + 8 = 12 + 8
This simplifies to:
x = 20
Therefore, the solution to the equation is x = 20.
Multiplying every term by 4x:
(4x)(1/4) - (4x)(2/x) = (4x)(3/x)
This simplifies to:
x - 8 = 12
Next, we isolate the variable x by adding 8 to both sides of the equation:
x - 8 + 8 = 12 + 8
This simplifies to:
x = 20
Therefore, the solution to the equation is x = 20.
How many degrees is 11pi/18
To convert radians to degrees, we use the formula:
Degrees = (Radians * 180) / π
In this case, we want to convert 11π/18 to degrees.
Degrees = (11π/18) * (180/π)
Simplifying:
Degrees = (11 * 180) / 18
Degrees = 1980 / 18
Degrees = 110
Therefore, 11π/18 is equal to 110 degrees.
Degrees = (Radians * 180) / π
In this case, we want to convert 11π/18 to degrees.
Degrees = (11π/18) * (180/π)
Simplifying:
Degrees = (11 * 180) / 18
Degrees = 1980 / 18
Degrees = 110
Therefore, 11π/18 is equal to 110 degrees.
Solve x^2-6x+13=0
To solve the quadratic equation x^2 - 6x + 13 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -6, and c = 13.
Substituting the values into the quadratic formula:
x = (6 ± √((-6)^2 - 4(1)(13))) / (2 * 1)
Simplifying:
x = (6 ± √(36 - 52)) / 2
x = (6 ± √(-16)) / 2
Since we have a negative value inside the square root, the equation does not have any real solutions. However, we can still find the solutions in terms of complex numbers by using the imaginary unit i, where i^2 = -1.
x = (6 ± √(-16)) / 2
x = (6 ± 4i) / 2
Simplifying further:
x = 3 ± 2i
Therefore, the solutions to the equation x^2 - 6x + 13 = 0 are x = 3 + 2i and x = 3 - 2i.
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -6, and c = 13.
Substituting the values into the quadratic formula:
x = (6 ± √((-6)^2 - 4(1)(13))) / (2 * 1)
Simplifying:
x = (6 ± √(36 - 52)) / 2
x = (6 ± √(-16)) / 2
Since we have a negative value inside the square root, the equation does not have any real solutions. However, we can still find the solutions in terms of complex numbers by using the imaginary unit i, where i^2 = -1.
x = (6 ± √(-16)) / 2
x = (6 ± 4i) / 2
Simplifying further:
x = 3 ± 2i
Therefore, the solutions to the equation x^2 - 6x + 13 = 0 are x = 3 + 2i and x = 3 - 2i.
given g=《3,-5》and h=《-4,6》, find 4g+3h
To find 4g + 3h, we first calculate 4g and 3h separately.
4g = 4 * ⟨3, -5⟩ = ⟨4*3, 4*(-5)⟩ = ⟨12, -20⟩
3h = 3 * ⟨-4, 6⟩ = ⟨3*(-4), 3*6⟩ = ⟨-12, 18⟩
Now, we add the corresponding components together:
4g + 3h = ⟨12, -20⟩ + ⟨-12, 18⟩ = ⟨12 + (-12), -20 + 18⟩ = ⟨0, -2⟩
Therefore, 4g + 3h = ⟨0, -2⟩.
4g = 4 * ⟨3, -5⟩ = ⟨4*3, 4*(-5)⟩ = ⟨12, -20⟩
3h = 3 * ⟨-4, 6⟩ = ⟨3*(-4), 3*6⟩ = ⟨-12, 18⟩
Now, we add the corresponding components together:
4g + 3h = ⟨12, -20⟩ + ⟨-12, 18⟩ = ⟨12 + (-12), -20 + 18⟩ = ⟨0, -2⟩
Therefore, 4g + 3h = ⟨0, -2⟩.