Advertisements
Advertisements
प्रश्न
Let z1 and z2 be two complex numbers such that `barz_1 + ibarz_2` = 0 and arg(z1 z2) = π. Then find arg (z1).
Advertisements
उत्तर
Given that `barz_1 + ibarz_2` = 0
⇒ z1 = iz2
i.e., z2 = –iz1
Thus arg (z1 z2) = argz1 + arg(–iz1) = π
⇒ arg`(-iz_1^2)` = π
⇒ arg(–i) + arg`(z_1^2)` = π
⇒ arg(–i) + 2arg (z1) = π
⇒ `(-pi)/2 + 2` arg(z1) = π
⇒ arg(z1) = `(3pi)/4`
APPEARS IN
संबंधित प्रश्न
Find the modulus and the argument of the complex number `z = – 1 – isqrt3`
Find the modulus and the argument of the complex number `z =- sqrt3 + i`
Convert the given complex number in polar form: – 1 + i
Convert the given complex number in polar form: – 1 – i
Convert the given complex number in polar form: –3
Convert the given complex number in polar form: i
Convert the following in the polar form:
`(1+7i)/(2-i)^2`
Convert the following in the polar form:
`(1+3i)/(1-2i)`
If the imaginary part of `(2z + 1)/(iz + 1)` is –2, then show that the locus of the point representing z in the argand plane is a straight line.
If |z| = 2 and arg(z) = `pi/4`, then z = ______.
The locus of z satisfying arg(z) = `pi/3` is ______.
What is the polar form of the complex number (i25)3?
The amplitude of `sin pi/5 + i(1 - cos pi/5)` is ______.
Show that the complex number z, satisfying the condition arg`((z - 1)/(z + 1)) = pi/4` lies on a circle.
If arg(z – 1) = arg(z + 3i), then find x – 1 : y. where z = x + iy.
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = `pi/2`, then show that `barz`w = –i.
arg(z) + arg`barz (barz ≠ 0)` is ______.
If |z| = 4 and arg(z) = `(5pi)/6`, then z = ______.
Find principal argument of `(1 + i sqrt(3))^2`.
|z1 + z2| = |z1| + |z2| is possible if ______.
The value of arg (x) when x < 0 is ______.
If arg(z) < 0, then arg(–z) – arg(z) = ______.
