Find The Complex Numbers Z Which Simultaneously Satisfy The Equation                        .

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

 

Find the complex numbers z which simultaneously satisfy the equation  

                     .

Solution

Correct option is

z1 = 6 + 8iz2 = 6 + 17i

  

   

  

  

The above equations can be written as   

          

   

     

              

  

and putting in (i), we get  

             

   

.

Hence  z1 = (6, 8) and z2­ = (6, 17)   

i.e.,   z1 = 6 + 8i and z2 = 6 + 17i are two solution.

Testing

SIMILAR QUESTIONS

Q1

If ω is fifth root of unity, then  

     

Q2

, then find the equation whose roots are p and q.

Q3

Find the roots of the equation , whose real part is negative.

Q4

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin. Then n must be of the form

  

Q6
Q7

For all complex numbers z1z2 satisfying , the minimum value of 

Q8

, show that z1z2z3 are the vertices of an equilateral triangle inscribed in a unit circle. 

Q9

The complex numbers z1, z2 and z3 satisfying  are the vertices of a triangle which is

Q10