If z be a complex number satisfying \left | Re\left ( z \right ) \right |+\left | Im(z) \right |=4, then \left | z \right | cannot be : 
Option: 1 \sqrt{7}
 
Option: 2 \sqrt{\frac{17}{2}}
 
Option: 3 \sqrt{10}
 
Option: 4 \sqrt{8}
 
 

Answers (1)

 

 

Complex number -

A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form as a + bi where a is the real part and b is the imaginary part. For example, 5 + 2i is a complex number. So, too, is 3 + 4i√3.

 

 

We write the complex number by C or z = a + ib, a and b are real number (a, b ∈ R).

  • a is real part of the complex number and denoted by Re(z), 

  • b is the imaginary part of the complex number and denoted by Im(z), 

E.g :    z = 2 + 3i is a complex number.

With Re(z) = 2 and Im(z) = 3

-

 

 

Area of triangle, circle (formula) -


Equation of Circle:

The equation of the circle whose center is at the point z_0  and have radius r is given by

|z-z_0| = r   

If the center is origin then, z_0=0, hence equation reduces to |z| = r

Interior of the circle is represented by |z-z_0| < r  

The exterior is represented by |z-z_0| > r

Here z can be represented as x + iy and z_0 is represented by  x_0 + iy_0

 

-

 

 

z = x + iy

|x| + |y| = 4

Minimum value of |z| = 2\sqrt2

Maximum value of |z| = 4

z\in[\sqrt8,\sqrt{16}]

So |z| can't be \sqrt7

Correct Option (1)

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