The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?
To solve this problem, let’s assume that the two complex numbers are represented as follows:
a + bi and c + di
where a, b, c, and d represent real numbers, and i is the imaginary unit
To solve this problem, let’s assume that the two complex numbers are represented as follows:
a + bi and c + di
where a, b, c, and d represent real numbers, and i is the imaginary unit.
According to the problem, the sum of these two complex numbers is equal to 34i:
(a + bi) + (c + di) = 34i
To find out what must be true about the complex numbers, we need to consider two components: the real part and the imaginary part.
For the real part of the equation, we add the real parts of the complex numbers:
(a + c) + (b + d)i = 34i
Since the real numbers do not equal zero (as stated in the problem), the real part of the equation cannot be equal to zero. Therefore, a + c ≠ 0.
Now, let’s consider the imaginary part of the equation:
(a + c) + (b + d)i = 34i
For the imaginary part to be equal to 34i, we need to have b + d = 34.
Therefore, the statement that must be true about the complex numbers is:
The sum of the real parts (a + c) must not be equal to zero, and the sum of the imaginary parts (b + d) must equal 34.
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