turkey-yks 2011 Q20

turkey-yks · Other · lys1-math Complex Numbers Arithmetic True/False or Property Verification Statements

For complex numbers $z = a + b i ( b \neq 0 )$ and $w = c + d i$, if the sum $\mathbf { Z } + \mathbf { W }$ and the product $\mathbf { Z } \cdot \mathbf { W }$ are both real numbers, then I. $z$ and $w$ are conjugates of each other. II. $\mathrm { z } - \mathrm { w }$ is real. III. $z ^ { 2 } + w ^ { 2 }$ is real. Which of the following statements are true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III

For complex numbers $z = a + b i ( b \neq 0 )$ and $w = c + d i$, if the sum $\mathbf { Z } + \mathbf { W }$ and the product $\mathbf { Z } \cdot \mathbf { W }$ are both real numbers, then\\
I. $z$ and $w$ are conjugates of each other.\\
II. $\mathrm { z } - \mathrm { w }$ is real.\\
III. $z ^ { 2 } + w ^ { 2 }$ is real.\\
Which of the following statements are true?\\
A) Only I\\
B) Only II\\
C) I and III\\
D) II and III\\
E) I, II and III

Paper Questions

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