Complex Number Question 5
Question 5 - 29 January - Shift 1
For two non-zero complex number $z_1$ and $z_2$, if $Re(z_1 z_2)=0$ and $Re(z_1+z_2)=0$, then which of the following are possible ?
(A) $Im(z_1)>0$ and $Im(z_2)>0$
(B) $Im(z_1)<0$ and $Im(z_2)>0$
(C) $Im(z_1)>0$ and $Im(z_2)<0$
(D) $Im(z_1)<0$ and $Im(z_2)<0$
Choose the correct answer from the options given below :
(1) B and D
(2) B and C
(3) $A$ and $B$
(4) A and C
Show Answer
Answer: (2)
Solution:
Formula: Algebra of complex numbers
$z_1=x_1+iy_1$
$z_2=x_2+iy_2$
$Re(z_1 z_2)=x_1 x_2-y_1 y_2=0$
$Re(z_1+z_2)=x_1+x_2=0$
$x_1 $ and $x_2$ are of opposite sign
$y_1 $ and $ y_2$ are of opposite sign
