Question

1) (3-2j)+(1+3j) 2) (5+j)-(3-2j) 3) (-3+2j)+5 4) 4(-1-j)-2(-3-2j) 5) 3j(j-4)-12j₁₂ 6) типо уравнение 3-3j ----- 1+j

Answer 1

Пошаговое объяснение:

1) (3-2j) +(1+3j) = 4+j

2) (5+j)-(3-2j)= 2+3j

3) (-3+2j)+5=2(1+j)

4) 4(-1-j)-2(-3-2j)= 2

Answer 2

1. To add complex numbers, you simply add their real parts and imaginary parts separately.

For (3-2j) + (1+3j): Real part: 3 + 1 = 4 Imaginary part: -2j + 3j = j

So, the sum is 4 + j.

2. To subtract complex numbers, you subtract their real parts and imaginary parts separately.

For (5+j) - (3-2j): Real part: 5 - 3 = 2 Imaginary part: j - (-2j) = j + 2j = 3j

So, the difference is 2 + 3j.

3. To add a real number to a complex number, you only add the real parts.

For (-3+2j) + 5: Real part: -3 + 5 = 2

The imaginary part remains unchanged, so the result is 2 + 2j.

4. To perform multiplication with complex numbers, you distribute the terms and use the fact that j^2 = -1.

For 4(-1-j) - 2(-3-2j): Multiplying the first term: 4(-1) - 4j = -4 - 4j Multiplying the second term: -2(-3) - 2(-2j) = 6 + 4j

Now, we can combine like terms: (-4 - 4j) - (6 + 4j) = -4 - 4j - 6 - 4j = -10 - 8j

So, the result is -10 - 8j.

5. To simplify the expression involving complex numbers, you need to apply the rules of complex arithmetic.

For 3j(j-4) - 12j₁₂: Expanding the expression: 3j^2 - 12j - 12j₁₂

Remember that j^2 = -1, so: 3(-1) - 12j - 12j₁₂ = -3 - 12j - 12j₁₂

The result is -3 - 12j - 12j₁₂.

6. It seems you have an equation: (3 - 3j) / (1 + j).

To simplify this expression, you can multiply the numerator and denominator by the conjugate of the denominator, which is (1 - j).

[(3 - 3j) / (1 + j)] * [(1 - j) / (1 - j)] = [(3 - 3j)(1 - j)] / [(1 + j)(1 - j)] = [(3 - 3j - 3j + 3j^2)] / (1^2 - j^2) = [(3 - 3j - 3j - 3)] / (1 - (-1)) = [-6 - 6j] / 2 = -3 - 3j.

So, the simplified expression is -3 - 3j.