If - z 1- z 2- z 1- z 2- where z 1 and z 2 are different non-zero complex numbers- then -A- Rez1 - z2-0B- lmz1 - z2-0C- z1-z2-0D- None of these

The correct option is B |z_1 + z_2| = |z_1| + |z_2| ⇒ (z_1 + z_2)(z_1 + z_2) = |z_1|^2 + |z_2|^2 + 2|z_1||z_2| ⇒ z_1z_2 + z_2z_1 nbsp;= 2 |z_1||z_2| ⇒ Im(z_ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Conjugate of a Complex Number

If | z 1+ z 2...

Question

If $| z_{1} + z_{2} | = | z_{1} | + | z_{2} |$ where $z_{1}$ and $z_{2}$ are different non-zero complex numbers, then :

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

$| z_{1} + z_{2} | = | z_{1} | + | z_{2} |$ $\Rightarrow$ (z_1 + z_2)( $_{1} +_{2})$

= $| z_{1} |^{2} + | z_{2} |^{2} + 2 | z_{1} | | z_{2} |$

$\Rightarrow$ $z_{1}$ $_{2}$ + $z_{2}$ $_{1}$ = 2 | $z_{1}$ || $z_{2}$ |

$\Rightarrow$ Im( $z_{1}_{2}$ ) = 0 i.e.,Im $(\frac{z_{1}}{z_{2}} | z_{2} |^{2})$ = 0

$\Rightarrow$ Im $(\frac{z_{1}}{z_{2}})$ = 0.

Suggest Corrections

Similar questions

If $| z_{1} + z_{2} |^{2}$ = $| z_{1} - z_{2} |^{2}$ where $z_{1}$ and $z_{2}$ are non-zero complex numbers, then :

Q. If

| z_{1} + z_{2} | = | z_{1} | + | z_{2} |

where

z_{1}

and

z_{2}

are different non - zero complex number, then ?

Q. For any two complex numbers

z_{1}, z_{2}

we have

| z_{1} + z_{2} |^{2} = | z_{1} |^{2} + | z_{2} |^{2} .

Then

Q. If

z_{1}

and

z_{2}

are two non zero complex numbers, satisfying the equation

| z_{1} | = | z_{2} | + | z_{1} - z_{2} |,

then which of the following is/are true

Q. If

z_{1}

and

z_{2}

are two non-zero complex numbers such that

| z_{1} - z_{2} | = | | z_{1} | - | z_{2} | |

then

arg (z_{1}) - arg (z_{2}) =

Join BYJU'S Learning Program

If |z1+z2|=|z1|+|z2| where z1 and z2 are different non-zero complex numbers, then :

The correct option is B |z1+z2|=|z1|+|z2| ⇒ (z_1 + z_2)(¯¯¯¯¯z1+¯¯¯¯¯z2) = |z1|2+|z2|2+2|z1||z2| ⇒ z1¯¯¯¯¯z2 + z2¯¯¯¯¯z1 = 2 |z1||z2| ⇒ Im(z1¯¯¯¯¯z2) = 0 i.e.,Im (z1z2|z2|2) = 0 ⇒ Im(z1z2) = 0.

If $| z_{1} + z_{2} | = | z_{1} | + | z_{2} |$ where $z_{1}$ and $z_{2}$ are different non-zero complex numbers, then :