Question

Find the value of (1+i)(1+i2

)(1+i3​

Answer 1

Answer:

ANSWER

(1+i)(1+i2)(1+i3)(1+i 4)

we know i 2 =−1

i 3=−i

and i 4=1

then

(1+i)(1−1)(1−i)(1+1)⇒(1+i)(0)(1−i)(2)=0

solution

Answer 2

SOLUTION

TO DETERMINE

The value of

$\sf (1 + i)(1 + {i}^{2} )(1 + {i}^{3} )$

EVALUATION

We know that i represents the complex number satisfying the property that i² = - 1

Here the given expression is

$\sf (1 + i)(1 + {i}^{2} )(1 + {i}^{3} )$

We simplify it as below

$\sf (1 + i)(1 + {i}^{2} )(1 + {i}^{3} )$

$= \sf (1 + i)(1 - 1 )(1 + {i}^{2} .i)$

$= \sf (1 + i) \times 0 \times (1 - i)$

$= 0$

FINAL ANSWER

$\sf (1 + i)(1 + {i}^{2} )(1 + {i}^{3} ) = 0$

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