Question

2. (a) Use Proposition 10.3.1: Polar Multiplication in C (PMC) along with Theorem 10.4.1: De Moivre's Theorem (DMT) to compute (V3 - 1)20 (1 - 1)30 - Present your answer in two forms, namely standard and polar. (b) Compute the standard form and the absolute value of the number where a = arctan (2). 2 = 5 cos a+isin a'

Answer 1

((( - ))" 2) را( - )) ها (4) 2 - 2 + 2 ) دا(zi - زهد )) دار )21 - 2) کارند-) اردک - )ارع کارن دارد) - ها(وک - - - این کا 10 کر | (1-5) i (12)7 (- (3) 19 (کر ترکوند - 13 + i - - is) آکر (3) 1+ ) کرد اک2 :( ; + (5) 14 ) ( ذ ) +۱ )*(5) 2 + 2 - )۔ (14)"(13 - )نه - <i (۰) -2 (5) (145)

=4i(a)(1+)(1+1/3) - 16 (1+73+216) = Gil -2+zir) - 321-3253 Hence, standard form polar form xtiy = -323 - 1(32) reio => 8= 5x²tyr 0 = tan 92 V64, O- ola 11/6. 64 e b x= arctan (224) xataño (2/4) = 0.2838 z = 5 Cos (0.2838) fisin (0-2838) 0.96ti 0.28 5 (0.96-10-28) (0.96²-;20-282) 11 4.8-i (1.4) - こ 4.8-1.41 Standard from xaly = 4.8+1(-1.4) absolute values xty2 = 125 = 5

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