Let w = z + 1 z 2 − 3 z + 6 and z = 1 + i (where i = − 1 ), then ∣ w ∣ and amp w respectively are

w = 2 + i ( 1 + i ) 2 − 3 ( 1 + i ) + 6 = 2 + i 3 − i = 5 ( 3 − i ) ( 2 − i ) = 5 5 − 5 i = 1 − i Hence ∣ w ∣ = 2 and amp. w = − 4 π .

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minQB

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Let $w = \frac{z ^{2} - 3 z + 6}{z + 1}$ and $z = 1 + i$ (where $i = - 1$ ), then $∣ w ∣$ and amp w respectively are

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Solution:

$w = \frac{( 1 + i ) ^{2} - 3 ( 1 + i ) + 6}{2 + i} = \frac{3 - i}{2 + i} = \frac{( 3 - i ) ( 2 - i )}{5} = \frac{5 - 5 i}{5} = 1 - i$ Hence $∣ w ∣ = 2$ and amp. $w = - \frac{π}{4}$ .

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: QB

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