Question

Z=(3-2i)^2-i^4комплексные числа

Answer 1

Z=9-12i-4i²-i⁴=9-12i+4+1=14-12i

Answer 2

To find the value of the expression Z = (3 - 2i)^2 - i^4, we'll first simplify the components step by step:

1. Simplify (3 - 2i)^2: (3 - 2i)^2 = (3 - 2i)(3 - 2i) Using the FOIL method (First, Outer, Inner, Last): = 3 * 3 + 3 * (-2i) + (-2i) * 3 + (-2i) * (-2i) = 9 - 6i - 6i + 4i^2

Since i^2 = -1, we can replace it in the expression: = 9 - 12i + 4(-1) = 9 - 12i - 4 = 5 - 12i

2. Now, calculate i^4: i^4 = (i^2)^2 Since i^2 = -1: i^4 = (-1)^2 i^4 = 1

3. Finally, substitute the value of i^4 into Z: Z = (3 - 2i)^2 - i^4 Z = (5 - 12i) - 1 Z = 5 - 12i - 1 Z = 4 - 12i

So, the value of Z is 4 - 12i.