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Complex Analysis
find the laplace transform of y"-4y'+9y=t, y(0)=0,y'(0)=1
Complex Analysis
Find the Laplace transform of y"-4y'+9y=t ,y(0)=0,y'(0)=1
Complex Analysis
Given that z= 1+i√2, express in the form a+bi each of the complex numbers p=z+1/z, q=z-1/z. In an Argand diagram, P and Q are the points which represent p and q respectively, O is the origin, M is the midpoints of PQ and G is the point on OM such that OG=(2/3)OM. Prove that angle PGQ is a right angle.
Complex Analysis
(1) Express -1+i in polar form. Hence show that (-1+i)^16 is real and that 1/(-1+i)^6 is purely imaginary, giving the value for each.
(2) Express sin5α and cos5α/cosα in terms of sinα
(2) Express sin5α and cos5α/cosα in terms of sinα
Complex Analysis
Find the module and the principal argument of W, z, wz and w/z, given that
(a) w=10i, z=1+i√3
(b) w= -2√3 +2i, z=1-i
(a) w=10i, z=1+i√3
(b) w= -2√3 +2i, z=1-i
Complex Analysis
Express sin 5θ and cos 5θ/ cos θ in terms of sin θ
Complex Analysis
Express −1+i in polar form. Hence show that (−1+i)16 is real and that 1/(−1+i)6 is purely imaginary, giving the value for each.
Complex Analysis
Use De Moivre’s theorem to simplify the following (a) (cos π/5+i sin π/5)10, (b) (cos π/9+i sin π/9)−3, (c) {cos(−π/6) + i sin(−π/6)}−4,
Complex Analysis
9. Find the moduli and principal arguments of w, z, wz and w/z, given that (a) w = 10i, z = 1 + i
3 + 2i, z = 1 − i, (c) w = , . 1 1 + i √
3 + 2i, z = 1 − i, (c) w = , . 1 1 + i √
Complex Analysis
Simplify the following expressions: (a) (cos π/4 + i sin π/4)(cos 3π/4 + i sin 3π/4), (b)
√ 3, (b) w = −2 1 √
(cos π/4 + i sin π/4)2 (cos π/6 + i sin π/6)
√ 3, (b) w = −2 1 √
(cos π/4 + i sin π/4)2 (cos π/6 + i sin π/6)
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