Question

Express the complex number in the standard form a + bi.

2i^7+6i^7+7i^18-3i^16+4i^24

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Answer 1

Answer:

The required expression of the given complex number is - 6 - 8i.

Step-by-step-explanation:

We have given a complex number.

We have to express it in the standard form a + bi.

The given complex number is 2i⁷ + 6i⁷ + 7i¹⁸ - 3i¹⁶ + 4i²⁴.

For a complex number a + bi, i is an imaginary number such that i² = - 1.

We know that,

i² = - 1

i³ = i² * i = - 1 * i = - i

i⁴ = ( i² )² = ( - 1 )² = 1

Now,

2i⁷ + 6i⁷ + 7i¹⁸ - 3i¹⁶ + 4i²⁴

⇒ 2 ( i⁴ * i³ ) + 6 ( i⁴ * i³ ) + 7 ( i¹⁶ * i² ) - 3i⁽ ⁴ * ⁴ ⁾ + 4i⁽ ⁴ * ⁶ ⁾ - - - [ aᵐ ⁺ ⁿ = aᵐ * aⁿ ]

⇒ 2 * 1 * ( - i ) + 6 * 1 * ( - i ) + 7i⁽ ⁴ * ⁴ ⁾ * ( - 1 ) - 3 ( i⁴ )⁴ + 4 ( i⁴ )⁶

⇒ ( - 2i ) + ( - 6i ) + 7 ( i⁴ )⁴ * ( - 1 ) - 3 * ( 1 )⁴ + 4 * ( 1 )⁶

⇒ - 2i - 6i + 7 * ( 1 )⁴ * ( - 1 ) - 3 * 1 + 4 * 1

⇒ - 8i + 7 * 1 * ( - 1 ) - 3 + 4

⇒ - 8i - 7 + 1

⇒ - 8i - 6

⇒ - 6 - 8i

∴ The required expression of the given complex number is - 6 - 8i.