Question

 (i64 + i17 + i13 + i82)(i72 – i34).

Answer 1

(i⁶⁴ + i¹⁷ + i¹³ + i⁸²)(i⁷² - i³⁴) = [(i⁴)¹⁶ + i¹⁶·i + i¹²·i + i⁸⁰·i²][(i⁴)¹⁸ - i³²·i²] =
= (1 + i + i - 1)(1 + 1) = 2i·2 = 4i
Ответ: 4i. 

Answer 2

To simplify this expression, we need to use the distributive property of multiplication over addition. We can distribute i64 over the expression i72 – i34 as follows:

(i64 + i17 + i13 + i82)(i72 – i34)

= i64(i72) – i64(i34) + i17(i72) – i17(i34) + i13(i72) – i13(i34) + i82(i72) – i82(i34)

Now, we can simplify each term by multiplying the complex numbers:

= (4608i) – (2176i) + (1224i) – (442i) + (936i) – (442i) + (5904i) – (2656i)

= 912i

Therefore, (i64 + i17 + i13 + i82)(i72 – i34) simplifies to 912i.