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Question

Mathematics Question on Complex Numbers and Quadratic Equations

If z=41−iz = \frac{4}{1-i}, then zˉ\bar{z} is (where zˉ\bar{z} is complex conjugate of zz )

A

2(1+i)2 (1 + i)

B

(1+i)(1 + i)

C

21−i\frac{2}{1-i}

D

41+i\frac{4}{1+i}

Answer

41+i\frac{4}{1+i}

Explanation

Solution

z=41−iz=\frac{4}{1-i}
⇒z=41−i×1+i1+i\Rightarrow z=\frac{4}{1-i} \times \frac{1+i}{1+i}
=4(1+i)12−i2=2(1+i)=\frac{4(1+i)}{1^{2}-i^{2}}=2(1+i)
∴zˉ=2(1−i)×(1+i)1+i\therefore \bar{z}=\frac{2(1-i) \times(1+i)}{1+i}
=41+i=\frac{4}{1+i}