Question

1 + i + i2 + i3 is equal to​

Answer 1

Step-by-step explanation:

1+3i+3i

1+6i

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Answer 2

Answer:

$1 + i + {i}^{2} + {i}^{3}$ is equal to 0.

Step-by-step explanation:

Given,

$1 + i + {i}^{2} + {i}^{3}$

We want to find value of the given term.

We know,

${i}^{2} = - 1$

So,

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

This is a problem of Complex number of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Complex number:

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