Let A- B- C be three sets of complex numbers as given below- A- z- Im z - 1 -B- z- - z-2-i - 3 - C- z- Re 1-i z - -2-The number of elements in the set A- B- C is

The correct option is B 1 1) Im(z) gt;= 1 #160; #160; ⇒ y ≥ 1 #160; #160; #160; #160; #160; #160; #160; (i) #160; ...

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Byju's Answer

Standard XII

Mathematics

Position of a Point with Respect to Circle

Let A, B, C b...

Question

Let A, B, C be three sets of complex numbers as given below. $A = {z : I m (z) \geq 1}, B = {z : | z - 2 - i | = 3}, C = {z : R e ((1 - i) z) = \sqrt{2}}^{-}$
The number of elements in the set $A \cap B \cap C$ is

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Solution

The correct option is B $1$
1) Im(z) >= 1
$\Rightarrow$ y $\geq$ 1 -(i)
$\Rightarrow$ A line parallel to x- axis with 1 unit distance including all point with magnitude greater than 1.

2) |z - 2 - i | = 3
This is a circle with center (2,1) and radius equal to 3 units on argand plane. z lies on the circle itself.

3) Re((1 - i) z) = $\sqrt{2}$
$\Rightarrow$ x + y = $\sqrt{2}$

Using the diagram to plot the above three curves, Only 1 point falls in the shaded region which is a common region to all of the curves i.e. pt. A .

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Let A, B, C be three sets of complex numbers as given below. A={z:Im(z)≥1},B={z:|z−2−i|=3},C={z:Re((1−i)z)=√2}−The number of elements in the set A∩B∩C is

Let A, B, C be three sets of complex numbers as given below. $A = {z : I m (z) \geq 1}, B = {z : | z - 2 - i | = 3}, C = {z : R e ((1 - i) z) = \sqrt{2}}^{-}$
The number of elements in the set $A \cap B \cap C$ is