Express 3.25 in the form of p/q
A) \(\frac{13}{4}\)
B) \(\frac{65}{2}\)
C) \(\frac{13}{40}\)
D) \(\frac{13}{20 }\)
2 Answers
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Simplify each of the following and express it in the form a + ib : `{:((i),2(3+4i)+i(5-6i),(ii),(3+sqrt(-16))-(4-sqrt(-9))),((iii),(-5+6i)-(2+i),(iv),
Correct Answer - `{:((i),(12+13i),(ii),(-1+7i),(iii),(-3+5i),(iv),"(11-9i)"),((v),(9+22i),(vi),28,(vii),(18-i),(vii),-7sqrt(3)i):}`
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Express each of the following in the form (a + ib) : `{:((i),(1)/((4+3i)),(ii),((3+4i))/((4-5i)),(iii),((5+sqrt(2)i))/((1-sqrt(2)i))),((iv),((-2+5i))/
Correct Answer - `{:((i),((4)/(25)-(3)/(25)i),(ii),((-8)/(41)+(31)/(41)i),(iii),(1+2 sqrt(2)i),"(iv)",((-4)/(5)+(1)/(15)i)),((v),((1)/(4)-(3)/(4)i),(vi),((63)/(25)-(16)/(25)i),(vii),((-22)/(5)+(19)/(5)i),"(vii)",(-2+0i)),((ix),((-7)/(2)+(1)/(2)i),,,,,,):}`
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Express each of the following in the form (a + ib) and find its conjugate: `{:((i),(1)/((4+3i)),(ii),(2+3i)^(2),(iii),((2-i))/((1-2i)^(2))),((iv),((1+
Correct Answer - `{:((i),z=((4)/(25)-(3)/(25)i)","bar(z)=((4)/(25)+(3)/(25)i),(ii),z=(-5+12i)","bar(z)=(-5-12i)),((iii),z=((-2)/(25)+(11)/(25)i)","bar(z)=((-2)/(25)-(11)/(25)i),(iv),z=((4)/(5)+(3)/(5)i)","bar(z)=((4)/(5)-(3)/(5)i)),((v),z=((7)/(25)+(24)/(25)i)","bar(z)=((7)/(25)-(24)/(25)i),(vi),z=(-1+i)","z^(-1)=((-1)/(2)-(1)/(2)i)):}`
2 Answers 1 views
Express each of the following in the form (a + ib) and find its multiplicative inverse : (i) `(1+2i)/(1-3i)`(ii) `((1+7i))/((2-i)^(2))`(iii) `(-4)/((1
Correct Answer - `{:((i),z=((-1)/(2)+(1)/(2)i)","z^(-1)=(-1-i),(ii),z=(-1+i)","z^(-1)=((-1)/(2)-(1)/(2)i)),((iii),z=(-1+i sqrt(3))","z^(-1)=((-1)/(4)-(sqrt(3))/(4)i),,):}`
2 Answers 1 views
Find the modulus and argument of each of the following complex numbers and hence express each of them in polar form: 4
Correct Answer - `4, 0, 4(cos 0 + i sin 0)`
2 Answers 10 views
Find the modulus and argument of each of the following complex numbers and hence express each of them in polar form: -2
Correct Answer - `2, pi, 2(cos pi + i sin pi)`
2 Answers 1 views
(i) Express 5 cm in metre and kilometre (ii) Express 35 mm in cm, m and km
Correct Answer - (i) `0.05 m, 0.00005 km " (ii) " 3.5 cm, 0.035 m, 0.000035 km`
2 Answers 1 views
Express the following complex number in polar form and exponential form. -i
Let z = -i = 0 – i a = 0, b = -1 z lies on negative imaginary Y-axis. |z| = r = \(\sqrt{a^2+b^2}=\sqrt{0^2+(-1)^2}=1\) and θ = amp z = 270° = \(\frac{3\pi}2\) The polar form of z...
2 Answers 2 views
Express the following complex number in polar form and exponential form. -1
Let z = -1 = -1 + 0.i a = -1, b = 0 z lies on negative real X-axis. |z| = r = \(\sqrt{a^2+b^2}\) = \(\sqrt{(-1)^2+0^2}\) = 1 and θ = amp z = 180° = π The...
2 Answers 2 views
In an organisation, employees hesitate to express their feelings and suggestions. They do not take initiative to express their problems. Suggest the e
Correct Answer - Communication
2 Answers 1 views