Advertisements
Advertisements
Question
If |z| = 2 and arg(z) = `pi/4`, then z = ______.
Solution
If |z| = 2 and arg(z) = `pi/4`, then z = `underlinebb(sqrt(2) (1 + i)`.
Explanation:
z = `|z|(cos pi/4 + isin pi/4)`
= `2(1/sqrt(2) + i 1/sqrt(2))`
= `sqrt(2) (1 + i)`
APPEARS IN
RELATED QUESTIONS
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: – 1 – i
Convert the given complex number in polar form `sqrt3 + 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.
The locus of z satisfying arg(z) = `pi/3` is ______.
What is the polar form of the complex number (i25)3?
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.
z1 and z2 are two complex numbers such that |z1| = |z2| and arg(z1) + arg(z2) = π, then show that z1 = `-barz_2`.
If for complex numbers z1 and z2, arg (z1) – arg (z2) = 0, then show that `|z_1 - z_2| = |z_1| - |z_2|`.
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
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.
|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) = ______.
