Reciprocal

Calculate reciprocal of z=0.8-1.8i:

Correct result:

Re =  0.21
Im =  0.46

Solution:

1z=10.8−1.8i=10.8−1.8i.0.8+1.8i0.8+1.8i Re1z=0.80.82+(−1.8)2=0.21\dfrac1z = \dfrac1{ 0.8-1.8i} = \dfrac1{ 0.8-1.8i} . \dfrac{ 0.8+1.8i}{ 0.8+1.8i} \ \\ Re \dfrac1z = \dfrac{ 0.8} { 0.8^2 + (-1.8)^2 } = 0.21
Im1z=−−1.80.82+(−1.8)2=0.46 1z=0.21+0.46iIm \dfrac1z = - \dfrac{ -1.8} { 0.8^2 + (-1.8)^2 } = 0.46 \ \\ \dfrac1z = 0.21 +0.46 i

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