Home
Class 12
MATHS
The point P represnets a complex number ...

The point P represnets a complex number z in the Argand plane. If the amplitude of z is `(pi)/(4)`, determine the locus of P.

Text Solution

Verified by Experts

Let `z=x+iy`
By hypthesis,amplitude of `z=(pi)/(4)`
Hence `tan^(-1)((y)/(x))=(pi)/(4) and (y)/(x) "tan"(pi)/(4)`
Hence `tan^(-1)((y)/(x))=(pi)/(4) and (y)/(x) = "tan" (pi)/(4)`
Hence x=y
`:.` The lcous of P is x=y
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -1 (A)|11 Videos

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -1 (B)|37 Videos

  • CIRCLE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 1(e)|25 Videos

  • DE MOIVRE'S THEOREM

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Long Answer Questions|6 Videos

Similar Questions

Explore conceptually related problems

If the amplitude of (z-1)"is" (pi)/(2) , then find the locus of z.

If the amplitude of (z-1-2i) "is" pi/3 , then the locus of z is

If |z-3+i|=4 determine the locus of z.

If the amplitude of ((z-2)/(z-6)) is (pi)/(3) , find its locus.

If the amplitude of z - 2 - 3i " is " pi//4 , then the locus of z = x +iy is

If the amplitude of ((z-2)/(z-6i))=(pi)/(2) find its locus.

Let z=x+iy and a point P represent z in the Argand plane. If the real part of (z-1)/(z+i) is 1, then a point that lies on the locus of P is

If a point p dentes a complex number z=x+iy in the argand plane and if (z+1)/(z+i) is a purely real number , then the locus of p is

z=x+iy represent a point in the Argand plane, find the locus of z. such that |z|=2

If z = x +iy and P represents z in the Argand plane and mod (2z-3) = 4 , then the locus of P is