Let S - z - z -1- z - C - Consider a function f - S - C defined as f z - z z- then f z maps S to which one of the following in thecomplex plane -A- unit circleB- horizontal axis line segment from origin to 1-0C- the point 1-0D- the entire horizontal axis

Let f(z) = u+iv f(z)=zz̅=|z|^2 = 1+i 0 ⇒ u=1, v=0 ∴ The set S are mapped to the point (1,0) in complex plane. ...

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Standard XII

Mathematics

Section Formula

Let S = z :| ...

Question

Let $S = {z : | z | = 1, z \in C}$ . Consider a function $f : S \to C$ defined as $f (z) = z ¯ z$ , then $f (z)$ maps $S$ to which one of the following in the complex plane ?

unit circle

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horizontal axis line segment from origin to

(1, 0)

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the point

(1, 0)

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the entire horizontal axis

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Solution

The correct option is C the point $(1, 0)$
Let $f (z) = u + i v$
$f (z) = z ¯ z = | z |^{2} = 1 + i 0 \Rightarrow u = 1, v = 0$

$∴$ The set $S$ are mapped to the point $(1, 0)$ in complex plane.

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Let S={z:|z|=1, z∈C}. Consider a function f:S→C defined as f(z)=z¯z, then f(z) maps S to which one of the following in the complex plane ?

The correct option is C the point (1,0)Let f(z)=u+iv f(z)=z¯z=|z|2=1+i0⇒u=1, v=0 ∴ The set S are mapped to the point (1,0) in complex plane.

Let $S = {z : | z | = 1, z \in C}$ . Consider a function $f : S \to C$ defined as $f (z) = z ¯ z$ , then $f (z)$ maps $S$ to which one of the following in the complex plane ?

The correct option is C the point $(1, 0)$
Let $f (z) = u + i v$
$f (z) = z ¯ z = | z |^{2} = 1 + i 0 \Rightarrow u = 1, v = 0$

$∴$ The set $S$ are mapped to the point $(1, 0)$ in complex plane.