Solve problems 2,3,4,and 5 for me please.

Amazing fact #2 If w is any complex number, the infinite series 1 + w w 2 w + ... = ow 2! 31 4! Notice this equation is true for w = 0 since e' = 1 and 1 + 0 + 0+0+ ... =1. Notice this holds for w = 1 by Amazing Fact #1. Amazing Fact #3 (1) 2. Suppose w = -1 in Amazing Fact #2. Write the first thirteen terms of the infinite series expansion of e raised to the power of -1. Powers of i should be simplified. Double check you only report thirteen terms. Amazing Fact #4 (1) 3. If w = i in Amazing Fact #2, then e' = O! T 1! 2! 3! 1 12 4! 5! + 6! 7! 8 ! 10 ! + ...... 11! 12 ! We can simplify this just a little using powers of i, where i = -1, is = -i, etc. Rewrite the expansion with simplified numerators of + i or + 1, by carefully completing the boxes below. e = 1 i 1 O! 1! 2 ! 3 ! 4 ! 5 ! 7! 8 ! 91 + ...... 10! 11! 12! (i) 4. Suppose w = iz in Amazing Fact #2, where z is any complex number. Write the first thirteen terms of the infinite series expansion of e raised to the power of iz. Powers of i should be simplified. Double check you only report thirteen terms. iz e Amazing fact #5 If w is any complex number in radians, the infinite series 1 w + wo w 8 W/ 14 O! 2 ! 4! 6 ! 8 ! 10! 12! 14 ! + ... = Cos w Notice this is true for w = 0 since cos 0 = 1 - 0 + 0 -0+ ... = 1 Amazing fact #6 If w is any complex number in radians, the infinite series w w ws w' will W 13 wis 1 ! 3 ! 5 ! 7! 9 ! 11! 13! 15 ! + ... = sin w Notice this is true for w = 0 since sin 0 = 0- 0+0-0+... =0 Amazing facts #7 and #8 (27) 5. Complete the boxes with simplified numerators of + i or + 1 to find the value of sin i and cos i. Powers of i should be simplified. cosi = + ...... 0! 2! 4! 6! B! sini = + .. .. =) + ... 1! 3! 5! 7! 9! 1 1 1! 3! 5! 7! 9! 11