Question

If |$z_1$| = 1, |$z_2$| = 2, |$z_3$| = 3 and |$9z_1{z}_2+4z_1{z}_3$| = 12, then the value of |$z_1$ + $z_2$ + $z_3$| is equal to:

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is A

2

|$z_1$| = 1, |$z_2$|= 2, |$z_3$|=3

$\Rightarrow$ $z_1$$\overline{z_1}$ = 1, $z_2$$\overline{z_2}$ = 4, $z_3$$\overline{z_3}$ = 9

$\Rightarrow$ |9$z_1{z}_2$ + 4$z_1{z}_3$ + $z_2{z}_3$| = 12

$\Rightarrow$ |$z_1{z}_2{z}_3$$\overline{z_3}$ + $z_1{z}_3{z}_2$$\overline{z_2}$ + $z_2{z}_3{z}_1$$\overline{z_1}$| = 12

$\Rightarrow$ |$z_1{z}_2{z}_3$($\overline{z_1}+\overline{z_2}+\overline{z_3})$| = 12

$\Rightarrow$ |$z_1$|| $z_2$ || $z_3$ || ${\overline{z}}_1\overline{+}\overline{z_2}\overline{+}\overline{z_3}$ | = 12

$\Rightarrow$ 6|$z_1$ + $z_2$ + $z_3$| = 12

$\Rightarrow$ |$z_1$ + $z_2$ + $z_3$| =2