JEE MAIN - Mathematics (2020 - 9th January Evening Slot - No. 5)
If z be a complex number satisfying
|Re(z)| + |Im(z)| = 4, then |z| cannot be :
$$\sqrt {10} $$
$$\sqrt {7} $$
$$\sqrt {{{17} \over 2}} $$
$$\sqrt {8} $$
Explanation
Let z = x + iy
given that |Re(z)| + |Im(z)| = 4
$$ \therefore $$ |x| + |y| = 4_9th_January_Evening_Slot_en_5_1.png)
Maximum value of |z| = 4
Minimum value of |z| = perpendicular distance of line AB from (0, 0) = $$2\sqrt 2 $$
$$ \therefore $$ |z| $$ \in $$ $$\left[ {2\sqrt 2 ,4} \right]$$
$$ \therefore $$ |z| cannot be $$\sqrt {7} $$.
given that |Re(z)| + |Im(z)| = 4
$$ \therefore $$ |x| + |y| = 4
Maximum value of |z| = 4
Minimum value of |z| = perpendicular distance of line AB from (0, 0) = $$2\sqrt 2 $$
$$ \therefore $$ |z| $$ \in $$ $$\left[ {2\sqrt 2 ,4} \right]$$
$$ \therefore $$ |z| cannot be $$\sqrt {7} $$.
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