Let z_1=3,z_2=2 and z_1+z_2+z_3=3+4i. If the real part of z_1z_2-+z_2z_3-+z_3z_1- is equal to 4, then z_3 is equal to (where, i^2=-1)

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) 2. |z^(1+z2+z3|2)=3^2+4^2=25 ⇒z_1+z_2+z_3z_1-+z_2-+z_3-=25 ⇒|z^(1|2)+|z^(2|2)+|z^(3|2)+z_1z_2-+z_2z_3-+z_3z_1-+z_1-z_2+z_2-z_3+z_3-z_1=25 ⇒9+4+z^32+z_1z_2-+z_2z_3-+z_3z_1-+z_1-z2+z_2-z_3+z_3-z_1=25 ⇒z^32+2real(z_1z_2-+z_2z_3-+z_3z_1-)=12 ⇒|z^(3|2)=4⇒z_3=2

Let $|z_{1}| = 3, |z_{2}| = 2$ and $z_{1} + z_{2} + z_{3} = 3 + 4 i$ . If the real part of $(z_{1} \bar{z_{2}} + z_{2} \bar{z_{3}} + z_{3} \bar{z_{1}})$ is equal to $4$ , then $|z_{3}|$ is equal to (where, $i^{2} = - 1$ )

Solution

More Complex Number Questions

Let z1=3,z2=2 and z1+z2+z3=3+4i. If the real part of z1z2-+z2z3-+z3z1- is equal to 4, then z3 is equal to (where, i2=-1)

Solution

More Complex Number Questions

Let $|z_{1}| = 3, |z_{2}| = 2$ and $z_{1} + z_{2} + z_{3} = 3 + 4 i$ . If the real part of $(z_{1} \bar{z_{2}} + z_{2} \bar{z_{3}} + z_{3} \bar{z_{1}})$ is equal to $4$ , then $|z_{3}|$ is equal to (where, $i^{2} = - 1$ )