Mayi please be assisted with the following problems.

ASSIGNMENT 02 Due date: Thursday, 30 April 2020 UNIQUE ASSIGNMENT NUMBER: 585426 ONLY FOR SEMESTER 1 INSTRUCTIONS FOR THE ASSIGNMENT Take care to explain all your arguments. If you choose to submit via my Unisa, note that only PDF files will be accepted. Problem 3. Find all the fourth roots of i and plot them on the Argand diagram. [5 marks Problem 4. Find all A E C such that: (2 - 32, 5 + 4i, -6 + 72) = (12 - 52, 7 + 22i, -32 - 92) 5 marks Problem 5. Let co and -co denote two distinct symbols, neither of which is in R. Define an addition and a multiplication on RU{co} U {-co} for each t E R by: OO. if t 0 - OO , if t > 0 t+ 0o = 00= 00 + t, t + (-00) = -00 = (-00) + t, 00 + 00 = 00 , (-00) + (-00) =-00, 00 + ( -00 ) = 0. Is RU {oo} U {-oo} a vector space over R? Explain. [5 marks] Problem 6. Show that in the definition of a vector space V the condition about existence of additive inverse can be replaced with the condition: Ov = v, for all v E V. Here the 0 on the left side of the equation is the scalar 0, and on right side of the equation is the additive identity of V. The phrase a condition can be replaced in a definition means that the collection of objects satisfying the definition is unchanged if the original condition is replaced with the new condition. [5 marks] [Total: 20 marks] - End of assignment 18