Home
Class 12
MATHS
If z1 = -3 + 5iota and z2 = 5 - 3iota an...

If z1 = -3 + 5`iota` and z2 = 5 - 3`iota` and z is a complex number lying on the line segment joining z1 & z2 then arg z can be

Text Solution

Verified by Experts

given that `z_1= -3+5i`
`z_2= 5- 3i`
`PQ = z_2 - z_1`
`= (5-3i)- (-3+5i) `
`= 8-8i`
`arg (PQ) = theta = tan^-1((img(PQ))/(real (PQ)))`
`= tan^-1(-8/8)= tan^-1(-1)`
`= -tan^-1 1 = -pi/4`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If z_1 = –3 + 5 i, z_2 = –5 – 3 i and z is a complex number lying on the line segment joining z_1 & z_2 , then arg(z) can be

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 ​ is equal to

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

If z_1 , z_2 and z_3 , z_4 are two pairs of conjugate complex numbers, then find arg( frac{z_1}{z_4} ) + arg( frac{z_2}{z_3} )

If z_1 and z_2 are two nonzero complex numbers such that |z_1-z_2|=|z_1|-|z_2| then arg z_1 -arg z_2 is equal to

If arg (z-z_1)/(z_2-z_1) = 0 for three distinct complex numbers z,z_1,z_2 then the three points are

Complex numbers z satisfy the equaiton |z-(4//z)|=2 The value of arg(z_(1)//z_(2)) where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, can be

Complex numbers z satisfy the equaiton |z-(4//z)|=2 The value of arg(z_(1)//z_(2)) where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, can be