If z is a non zero complex number- where z - 2-z- - i- then number of possible values of z is

Let z = x + iy Now, z + 2|z| = i ⇒x+ iy + 2√(x^2 + y^2) = i ⇒ x = 2 nbsp; So, y√(4 + y^2) = 1 ⇒ y = √(4 + y^2) ⇒ y^2 = 4 + y^2 Not possible nbsp; Hence no ...

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Standard XII

Mathematics

Geometrical Representation of Argument and Modulus

If z is a non...

Question

If $z$ is a non zero complex number, where $\frac{z + 2}{| z |} = i$ , then number of possible value(s) of $z$ is

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Solution

The correct option is A $0$
Let $z = x + i y$
Now,
$\frac{z + 2}{| z |} = i \Rightarrow \frac{x + i y + 2}{\sqrt{x^{2} + y^{2}}} = i \Rightarrow x = - 2$
So,
$\frac{y}{\sqrt{4 + y^{2}}} = 1 \Rightarrow y = \sqrt{4 + y^{2}} \Rightarrow y^{2} = 4 + y^{2}$
Not possible
Hence no complex number possible.

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If z is a non zero complex number, where z+2|z|=i, then number of possible value(s) of z is

The correct option is A 0Let z=x+iy Now, z+2|z|=i⇒x+iy+2√x2+y2=i⇒x=−2 So, y√4+y2=1⇒y=√4+y2⇒y2=4+y2 Not possible Hence no complex number possible.

If $z$ is a non zero complex number, where $\frac{z + 2}{| z |} = i$ , then number of possible value(s) of $z$ is