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Syllabus

^{6}+i^{7}+i^{8}+i^{9}/i^{2}+i^{3}Represent the following in polar form

1/1+i

If a+3i/2+ib=1-i, show that (5a-3b)=0.

if a+3i / 2+ ib = 1-i, show that (5a-7b) = 0

_{1}/Z_{2}l = 1 and arg (Z_{1}Z_{2}) = 0 then_{1}bar) = arg (Z_{2}) then^{35 }^{888 evaluate}show that (-1+root3i)

^{3}is a real number.^{2}) = 4^{10}+i^{20}+i^{30}show that is reali^{30}i^{40}i^{50}i^{60}^{2}-2(4k-1)x+15k^{2}-2k-70 is valid for anyreal x is??(2+3i)(1-4i)

Very confusing.

(A)

a= 0 (B) $a=\frac{40}{41}$ (C)b= 1 (D) $b=-\frac{9}{41}$7. The subset of complete set of values of k for which the expression x

^{2}-2(k-2) x-2k^{2}-5k+6 is always positive is.$\left(\mathrm{A}\right)\left(-1,\frac{2}{3}\right)\left(\mathrm{B}\right)\left(0,\frac{1}{2}\right)\left(\mathrm{C}\right)(-\infty ,-1]\cup [\frac{2}{3},\infty ),\left(\mathrm{D}\right)\left(\frac{2}{3},1\right)$