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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?

a.) The complex numbers have equally imaginary coefficients
b.) The complex numbers have equal real numbers.
c.) The complex numbers have opposite imaginary coefficients
d.) The complex numbers have opposite real numbers.

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d.) The complex numbers have opposite real numbers.

Example:

a = 3 + 20i and b = -3 + 14i

a + b = 3 + 20i + (-3) + 14i = 34i
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Answer:

Option d is correct.

Step-by-step explanation:

In general, a complex number is written as, [tex]a+ib[/tex] where a is real part and b is imaginary part.

Now, two complex numbers are added and their sum is [tex]34i[/tex] which can also be written as [tex]0+34i[/tex]. Here, the real part is zero.

It is also given that the real part of the complex number is not zero in both the cases.

Let us consider two complex numbers [tex]a+ib[/tex] and [tex]c+id[/tex].

Add the two complex numbers:

[tex](a+ib)+(c+id)=(a+c)+i(b+d)[/tex]

Now, the real part should be zero only when [tex]a=-c[/tex].

Therefore, the complex numbers must have opposite real part or numbers. Option d is correct.

For more details, refer the link:

https://brainly.com/question/20566728?referrer=searchResults

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