The greatest and the least value of $\left| {{z_1} + {z_2}} \right|,$ if ${z_1} = 24 + 7i$ and $\left| {{z_2}} \right| = 6,$ are respectively

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

The greatest and the least value of

\left| {{z_1} + {z_2}} \right|,

{z_1} = 24 + 7i

and

\left| {{z_2}} \right| = 6,

are respectively

View answer and explanation

Correct option: A

31,\;19

Option A (31, 19) is correct because the greatest value is the sum of the magnitudes and the least value is the difference of the magnitudes.

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}