The correct option is C 2 nbsp;( 1 i ) ^ 3 / 1 i^ 3 =( 1 i ) ^ 3 /( 1 i ) ( 1+ i ^ 2 +i ) nbsp; =( 1 i ) nbsp;^ 2 / i = 1+ i ^ 2 2i / i = ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

1-i 3/1-i3

Question

$\frac{{(1 - i)}^{3}}{1 - i^{3}}$

2

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- 2

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- 2 i

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Solution

The correct option is C $- 2$
$\frac{{(1 - i)}^{3}}{1 - i^{3}} = \frac{{(1 - i)}^{3}}{(1 - i) (1 + i^{2} + i)} = \frac{{(1 - i)}^{2}}{i} = \frac{1 + i^{2} - 2 i}{i} = - 2$
Ans: B

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Similar questions

(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i}) =

Q. Simplify

(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})

Q. Solve:

(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})

Q. Reduce

(\frac{1}{1 + 2 i} + \frac{3}{1 - i}) (\frac{3 - 2 i}{1 + 3 i})

to the form (a+ib).

Express the following complex numbers in the standard form a + i b :

$(i) (1 + i) (1 + 2 i) (i i) \frac{3 + 2 i}{- 2 + i} (i i i) \frac{1}{(2 + i)^{2}} (i v) \frac{1 - i}{1 + i} (v) \frac{(2 + i)^{3}}{2 + 3 i} (v i) \frac{(1 + i) (1 + \sqrt{3 i})}{1 - i} (v i i) \frac{2 + 3 i}{4 + 5 i} (v i i i) \frac{(1 - i)^{3}}{1 - i^{3}} (i x) (1 + 2 i)^{- 3} (x) \frac{3 - 4 i}{(4 - 2 i) (1 + i)} (x i) (\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{3 - 4 i}{5 + i}) (x i i) \frac{5 + \sqrt{2 i}}{1 - \sqrt{2 i}}$

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(1−i)31−i3

The correct option is C −2(1−i)31−i3=(1−i)3(1−i)(1+i2+i)=(1−i)2i=1+i2−2ii=−2Ans: B

$\frac{{(1 - i)}^{3}}{1 - i^{3}}$

The correct option is C $- 2$
$\frac{{(1 - i)}^{3}}{1 - i^{3}} = \frac{{(1 - i)}^{3}}{(1 - i) (1 + i^{2} + i)} = \frac{{(1 - i)}^{2}}{i} = \frac{1 + i^{2} - 2 i}{i} = - 2$
Ans: B