Final answer:
To solve the equations, the real and imaginary parts of the complex numbers are equated separately. For each equation, A, B, C, ..., H values are deduced by comparing these parts, resulting in specific numeric values for each letter.
Step-by-step explanation:
To solve for A, B, C, ..., H in the given complex number equations, we use the property that two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. For example, for the equation (6 * 7i) = A + jB, we compare the real and imaginary parts to find that A = 0 and B = 42, since 6 * 7i gives us 0 + 42i.
Following this approach with the additional equations will give us:
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- (3i * 4i) = C + iD: Here, 3i * 4i equals -12, therefore, C = -12 and D = 0.
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- i^9(9 + 7i) = E + iF: Since i^9 = i^(8+1) = i^8 * i^1 = 1 * i = i (as i^4 = 1 and multiples of 4 give us 1), this simplifies to 9i + 7i^2. Noting that i^2 = -1, we get 9i - 7, which yields E = -7 and F = 9.
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- (2 + 3i)(3 + 5i) = G + iH: Expanding the product we get 6 + 10i + 9i + 15i^2 which simplifies to 6 + 19i - 15, resulting in G = -9 and H = 19.
So the values are:
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- A = 0
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- B = 42
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- C = -12
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- D = 0
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- E = -7
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- F = 9
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- G = -9
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- H = 19