Question

if $Z_1$ and $Z_2$ are 2 non - complex number such that |$Z_1$ + $Z_2$| = |$Z_1$| + |$Z_2$|,Then arg ($Z_1$) - arg($Z_2$) is equal to

Hint: Square on both sides.

• A. - π
• B. π/2
• C. 0
• D. -π/2

Answer 1

The correct option is C

0

Given |$Z_1$ + $Z_2$| = |$Z_1$| + |$Z_2$|

Squaring on both sides,

$|Z_1+Z_2{|}^2$ = $|Z_1{|}^2$ + $|Z_2{|}^2$ + 2 |$Z_1$||$Z_2$|

$\Rightarrow$ = $|Z_1{|}^2$ + $|Z_2{|}^2$ + 2 |$Z_1$||$Z_2$| cos(arg $Z_1$ - arg$Z_1$) = $|Z_1{|}^2$ + $|Z_2{|}^2$ + 2 |$Z_1$||$Z_2$|

$\Rightarrow$ cos (arg $Z_1$ - arg$Z_1$) = 1

$\Rightarrow$ arg$Z_1$ = arg$Z_2$

So, C is right option.