Linear Algebra Questions and Answers 2

1. Equation: (2x + 3i) + (x - 2i) = 5 + i

Working Out:

Combine like terms:

3x + i = 5 + i

Subtract i from both sides to isolate the variable:

3x = 5

Divide both sides by 3 to find the value of x:

x=5/3

, 2. Equation: (3 + 4i)x = 9 - 6i

Working Out:

Divide both sides by (3 + 4i) to isolate the variable:

x = (9 - 6i) / (3 + 4i)

x = (9 - 6i)(3 - 4i) / (3 + 4i)(3 - 4i)

x = (27 - 36i - 18i + 24i^2) / (9 - 16i^2)

x = (27 - 54i - 24) / (9 + 16)

x = (3 - 6i) / 5

x = 3/5 - (6/5)i



3. Equation: |2x - 5i| = 3

Working Out:

For the absolute value to be 3, the expression inside the absolute value must be ±3:

2x - 5i = 3 or 2x - 5i = -3

Solve for x in both cases:

2x = 3 + 5i or 2x = -3 + 5i

x = (3 + 5i) / 2 or x = (-3 + 5i) / 2



4. Equation: (x + 2i)(x - 2i) = 12

Working Out:

Use the difference of squares formula to simplify the left side:

(x + 2i)(x - 2i) = x^2 - (2i)^2

(x + 2i)(x - 2i) = x^2 - 4i^2

(x + 2i)(x - 2i) = x^2 + 4

Now set the equation equal to 12:

x^2 + 4 = 12

Subtract 4 from both sides to isolate the variable:

x^2 = 8

Take the square root of both sides to find the two solutions for x:

x = ±√8

x = ±2√2