Home
Class 12
MATHS
If |z-(4 + 3i) |=1, then find the comple...

If `|z-(4 + 3i) |=1,` then find the complex number z for each of the following cases:
(i) `|z| ` is least
(ii) `|z|` is greatest
(iii) `arg(z)` is least
(iv) arg(z) is greatest

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ |z - (4 + 3i)| = 1 \] This represents a circle in the complex plane with center at \(C(4, 3)\) and radius \(1\). ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.2|9 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise ILLUSTRATION|110 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 arg(z) lt 0, then find arg(-z) -arg(z) .

If z ne 0 be a complex number and "arg"(z)=pi//4 , then

Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (ii) |z-1|le|z| |arg z | + |z|-1|

If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

The point representing the complex number z for which arg ((z-2)/(z+2))=pi/3 lies on

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

1. If |z-2+i|≤ 2 then find the greatest and least value of | z|

Complex number z lies on the curve S-= arg(z+3)/(z+3i) =-(pi)/(4)

1. If |z-2+i| ≤ 2 then find the greatest and least value of | z|

If arg(z-1)=arg(z+3i) , then find (x-1):y , where z=x+iy .