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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

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

^{3}is a real number.^{10}+i^{20}+i^{30}show that is reali_{1}bar) = arg (Z_{2}) then^{2}) = 4^{30}i^{40}i^{50}i^{60}^{2}-2(4k-1)x+15k^{2}-2k-70 is valid for anyreal x is??8) Express the following numbers in the form x + iy

i) $\sqrt{3}$ (cos $\frac{\mathrm{\pi}}{6}$ + isin $\frac{\mathrm{\pi}}{6}$)

ii) $\sqrt{2}$(cos $\frac{\mathrm{\pi}}{4}$ + isin $\frac{\mathrm{\pi}}{4}$)

(2+3i)(1-4i)

Thnkx!

Ans: 1.

How?

Very confusing.

(A)

a= 0 (B) $a=\frac{40}{41}$ (C)b= 1 (D) $b=-\frac{9}{41}$^{2}+ lzl^{2}= 0 where z belongs to complex numberHow?

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.$\left(\mathrm{A}\right)\left(-1,\frac{2}{3}\right)\left(\mathrm{B}\right)\left(0,\frac{1}{2}\right)\left(\mathrm{C}\right)(-\infty ,-1]\cup [\frac{2}{3},\infty ),\left(\mathrm{D}\right)\left(\frac{2}{3},1\right)$

Ans: opt A.

Ans: 2

How

Ans: BCD.