Home
Class 12
MATHS
If |z-i R e(z)|=|z-I m(z)| , then prove ...

If `|z-i R e(z)|=|z-I m(z)|` , then prove that `z` , lies on the bisectors of the quadrants.

Text Solution

AI Generated Solution

To prove that \( z \) lies on the bisectors of the quadrants given the equation \( |z - i \, \text{Re}(z)| = |z - i \, \text{Im}(z)| \), we will follow these steps: ### Step 1: Express \( z \) in terms of its real and imaginary parts Let \( z = x + iy \), where \( x = \text{Re}(z) \) and \( y = \text{Im}(z) \). ### Step 2: Substitute \( z \) into the given equation Substituting \( z \) into the equation gives: \[ ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.6|10 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.7|6 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.4|7 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

If |z-iRe(z)|=|z-Im(z)|, then prove that z lies on the bisectors of the quadrants, " where "i=sqrt(-1).

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If z_(2) be the image of a point z_(1) with respect to the line (1-i)z+(1+i)bar(z)=1 and |z_(1)|=1 , then prove that z_(2) lies on a circle. Find the equation of that circle.

If z = barz then z lies on

If z = (3)/( 2 + cos theta + I sin theta) , then prove that z lies on the circle.

If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r s inthetadot)

If "Re"((z-8i)/(z+6))=0 , then z lies on the curve

if Im((z+2i)/(z+2))= 0 then z lies on the curve :

If z = x + iy lies in the third quadrant, then prove that (barz)/(z) also lies in the third quadrant when y lt x lt 0

If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)