Home
Class 12
MATHS
If z(1) =3 -4i and z(2) = 5 + 7i,verify...

If ` z_(1) =3 -4i and z_(2) = 5 + 7i`,verify
(i) ` |-z_(1)| =|z_(1)|`
(ii) ` |z_(1) +z_(2)| lt |z_(2)|`

Text Solution

AI Generated Solution

To verify the given identities involving complex numbers \( z_1 = 3 - 4i \) and \( z_2 = 5 + 7i \), we will follow these steps: ### Part (i): Verify \( |-z_1| = |z_1| \) 1. **Calculate \( -z_1 \)**: \[ -z_1 = - (3 - 4i) = -3 + 4i \] ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If z_(1)=5+2i and z_(2)=2 +i ,verify (i) |z_(1)z_(2)|= |z_(1)||z_(2)|

If z_(1) = 4 -I and z_(2) = - 3 + 7i then find (i) z_(1) +z_(2) (ii) z_(1) -z_(2)

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |-z_(1)| = |z_(1)|

If z_(1) = 3+ 2i and z_(2) = 2-i then verify that (i) bar(z_(1) + z_(2)) = barz_(1) + barz_(2)

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

If z_(1) = 5 + 12i and |z_(2)| = 4 , then

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1)z_(2) |= |z_(1)| |z_(2)|

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)| lt |z_(1)| + |z_(2)|

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)z_(2)|= |z_(1)||z_(2)|

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)-z_(2)| gt |z_(1)|-|z_(2)|