Advertisements
Advertisements
प्रश्न
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
उत्तर
z = `(1 - i)/(cos pi/3 + i sin pi/3)`
= `(sqrt2[1/sqrt2 - i1/sqrt2])/(cos pi/3 + isin pi/3) =(sqrt2[cos(-pi/4) + isin(-pi/4)])/(cos pi/3 + isin pi/3)`
= `sqrt2[cos(-pi/4 - pi/3) + isin(-pi/4 - pi/3)]`
= `sqrt2[cos(-(7pi)/12) + isin(-(7pi)/12)]`
= `-sqrt2[cos (5pi)/12 + isin (5pi)/12]`
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 `sqrt3 + i`
Convert the given complex number in polar form: i
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.
Let z1 and z2 be two complex numbers such that |z1 + z2| = |z1| + |z2|. Then show that arg(z1) – arg(z2) = 0.
The locus of z satisfying arg(z) = `pi/3` is ______.
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.
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.
If |z| = 4 and arg(z) = `(5pi)/6`, then z = ______.
State True or False for the following:
Let z1 and z2 be two complex numbers such that |z1 + z2| = |z1| + |z2|, then arg(z1 – z2) = 0.
Find z if |z| = 4 and arg(z) = `(5pi)/6`.
Find principal argument of `(1 + i sqrt(3))^2`.
|z1 + z2| = |z1| + |z2| is possible if ______.
If arg(z) < 0, then arg(–z) – arg(z) = ______.
