MAT1581
SEMESTER 2
2020
ASSIGNMENT 02
MEMO
, Question 1
(3−5𝑗)(2−6𝑗)
2+4𝑗
first multiply the brackets on the numerator
3(2−6𝑗)−5𝑗(2−6𝑗)
2+4𝑗
6−18𝑗−10𝑗+30𝑗 2
2+4𝑗
𝑟𝑒𝑚𝑒𝑚𝑏𝑒𝑟 𝑗 2 = −1
6−28𝑗−30
2+4𝑗
−24−28𝑗
𝑛𝑜𝑤 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑏𝑦 𝑡ℎ𝑒 𝑐𝑜𝑛𝑗𝑢𝑔𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
2+4𝑗
−24−28𝑗 2−4𝑗
×
2+4𝑗 2−4𝑗
2(−24−28𝑗)−4𝑗(−24−28𝑗)
4−16𝑗 2
−48−56𝑗+96𝑗+112𝑗 2
4+16
−48+40𝑗−112
20
−160+40𝑗
20
−8 + 2𝑗
Question 2
𝑧 = 8(cos 225° + 𝑗 sin 225°)
3
𝑡ℎ𝑒 3 𝑐𝑢𝑏𝑒 𝑟𝑜𝑜𝑡𝑠 𝑚𝑒𝑎𝑛𝑠 √𝑧
𝑟 =8; 𝜃 = 225° ; 𝑛=3
𝐷𝑒 𝑀𝑜𝑖𝑣𝑟𝑒`𝑠 𝑇ℎ𝑒𝑜𝑟𝑒𝑚
SEMESTER 2
2020
ASSIGNMENT 02
MEMO
, Question 1
(3−5𝑗)(2−6𝑗)
2+4𝑗
first multiply the brackets on the numerator
3(2−6𝑗)−5𝑗(2−6𝑗)
2+4𝑗
6−18𝑗−10𝑗+30𝑗 2
2+4𝑗
𝑟𝑒𝑚𝑒𝑚𝑏𝑒𝑟 𝑗 2 = −1
6−28𝑗−30
2+4𝑗
−24−28𝑗
𝑛𝑜𝑤 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑏𝑦 𝑡ℎ𝑒 𝑐𝑜𝑛𝑗𝑢𝑔𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
2+4𝑗
−24−28𝑗 2−4𝑗
×
2+4𝑗 2−4𝑗
2(−24−28𝑗)−4𝑗(−24−28𝑗)
4−16𝑗 2
−48−56𝑗+96𝑗+112𝑗 2
4+16
−48+40𝑗−112
20
−160+40𝑗
20
−8 + 2𝑗
Question 2
𝑧 = 8(cos 225° + 𝑗 sin 225°)
3
𝑡ℎ𝑒 3 𝑐𝑢𝑏𝑒 𝑟𝑜𝑜𝑡𝑠 𝑚𝑒𝑎𝑛𝑠 √𝑧
𝑟 =8; 𝜃 = 225° ; 𝑛=3
𝐷𝑒 𝑀𝑜𝑖𝑣𝑟𝑒`𝑠 𝑇ℎ𝑒𝑜𝑟𝑒𝑚
