If - z -1- i -1 and - z - is least then z -A- -4B- 0D- -3

The correct option is C π4z = x + nbsp;iy ⇒|z 1+i|= |(x 1) + i(y+1)| nbsp;=1 ⇒ (x 1)^2+(y+1)^2 = 1 which is a circle of rad.=1 and centre (1, 1) ∴ z= π4 ...

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Byju's Answer

Standard XII

Mathematics

Geometrical Representation of Argument and Modulus

If | z -1+ i ...

Question

If $∣ z - 1 + i ∣= 1$ and $∣ z ∣$ is least then $arg z =$

0

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\frac{π}{4}

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\frac{- π}{4}

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\frac{- π}{3}

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Solution

The correct option is C $\frac{- π}{4}$
$z = x + i y \Rightarrow | z - 1 + i | = | (x - 1) + i (y + 1) | = 1$

$\Rightarrow (x - 1)^{2} + (y + 1)^{2} = 1$ which is a circle of rad. $= 1$ and centre $(1, - 1)$

$∴ arg z = \frac{- π}{4}$

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If ∣z−1+i∣=1 and ∣z∣ is least then argz=

The correct option is C −π4z=x+iy⇒|z−1+i|=|(x−1)+i(y+1)|=1 ⇒(x−1)2+(y+1)2=1 which is a circle of rad.=1 and centre (1,−1) ∴argz=−π4

If $∣ z - 1 + i ∣= 1$ and $∣ z ∣$ is least then $arg z =$

The correct option is C $\frac{- π}{4}$
$z = x + i y \Rightarrow | z - 1 + i | = | (x - 1) + i (y + 1) | = 1$

$\Rightarrow (x - 1)^{2} + (y + 1)^{2} = 1$ which is a circle of rad. $= 1$ and centre $(1, - 1)$

$∴ arg z = \frac{- π}{4}$