Question

The sum of two complex numbers, where the real numbers do not equal zero, results in the sum of 34i.Which statement must be true about complex numbers? (A.The complex numbers have equal 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.)

Answer 1

Let the complex numbers be a + bi and c + di

Sum is (a + c) + (b + d)i = 34i

Therefore a + c = 0. a = -c.

Thus, answer is option: D

Answer 2

Answer:

D. The complex numbers have opposite real numbers.

Step-by-step explanation:

Let the complex numbers = $a+ib$ and $c+id$, where a,b,c,d are non-zero real numbers

Now, it is given that,

Sum of these complex numbers is $34i$.

That is, we have,

$(a+ib)+(c+id)=34i$

i.e. $(a+c)+i(b+d)=34i$

i.e. $a+c=0$ and $b+d=34$

i.e. $a=-c$ and  $b+d=34$

So, we get that,

$a=-c$, that is, the real parts of the complex numbers are of opposite signs.

Hence, option D is correct.