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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 (3)

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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)

Posted by

avinash.dongre

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JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Options

Posted by

Shravani.D.K

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Option d

Posted by

Shravani.D.K

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