Home
Class 12
MATHS
Let z1=10+6i and z2=4+6idot If z is any ...

Let `z_1=10+6i` and `z_2=4+6idot` If `z` is any complex number such that the argument of `((z-z_1))/((z-z_2))` is `pi/4,` then prove that `|z-7-9i|=3sqrt(2)` .

Text Solution

Verified by Experts

Since `z_1 = 10 + 6i , z_2 = 4+ 6i`
and arg`((z-z_1)/(z-z_2))-(pi/4)` represente lecue of z is a circle shown as form the figure whose center is (7,y) and `angle AOB = 90^@` clearly OC = 9 `rArr` OD = 6 + 3 =9
`therefore ` Center = (7,9) and readius `= (6)/sqrt(2)=3 sqrt2`

`rArr` Equation of circle is `|z-(7 +9 i )|= 3sqrt(2)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 4 ROTATION OF A COMPLEX NUMBER (OBJECTIVE QUESTION I)(ONLY ONE CORRECT OPTION)|6 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 4 ROTATION OF A COMPLEX NUMBER (OBJECTIVE QUESTION II)(ONE OR MORE THAN ONE CORRECT OPTION)|2 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 3 ARGUMENT OF A COMPLEX NUMBER (OBJECTIVE QUESTIONS II)()|1 Videos

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 5 Integer Answer type Question|1 Videos

  • DEFINITE INTEGRATION

    IIT JEE PREVIOUS YEAR|Exercise LIMITS AS THE SUM|6 Videos

Similar Questions

Explore conceptually related problems

Let z_(1)=10+6i and z_(2)=4+6i. If z is a complex number such that the argument of (z-z_(1))/(z-z_(2))is(pi)/(4), then prove that |z-7-9i|=3sqrt(2)

Let z_(1)=6+i&z_(2)=4-3i Let z be a a complex number such that arg((z-z_(1))/(z-z_(2)))=(pi)/(2) then z satisfies

Let z_1=6+i and z_2=4-3i . If z is a complex number such thar arg ((z-z_1)/(z_2-z))= pi/2 then (A) |z-(5-i)=sqrt(5) (B) |z-(5+i)=sqrt(5) (C) |z-(5-i)|=5 (D) |z-(5+i)|=5

If z_1=10+6i and z_2=4+2i be two complex numbers and z be a complex number such that a r g((z-z_1)/(z-z_2))=pi/4 , then locus of z is an arc of a circle whose (a) centre is 5+7i (b) centre is 7+5i (c) radius is sqrt(26) (d) radius is sqrt(13)

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

Let Z_1 and Z_2 be any two non-zero complex number such that 3|z_1|= 4 |Z_2 |. If z =( 3z_1)/(2z_2)+(2z_2)/(3z_1) then

If z be any complex number (z!=0) then arg((z-i)/(z+i))=(pi)/(2) represents the curve

For complex numbers z_1 = 6+3i, z_2=3-I find (z_1)/(z_2)

IIT JEE PREVIOUS YEAR-COMPLEX NUMBERS-TOPIC 3 ARGUMENT OF A COMPLEX NUMBER (OBJECTIVE QUESTIONS II)(ANALYTICAL & DESCRIPTIVE QUESTIONS )
  1. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |