(cos30 – isin30)-3(cos50 + isin58) -2 Show that = cos 30 + i sin 30, (cos40...
Chi940 Test 9 Use De Moivre's Theorem to write [3(cos 80° + i sin 80°)] in arbi form where a and b exact values, are
2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" = cos(n θ) + j sin(ne). where n is an integer 217 Use de Moivre's formula, given by Eq. (2.80), to develop the rectangular and polar form representations of the (2.80) following complex numbers: 2.18 Show that 219 Determine the roots of the following second-degree polynomials (a) (G)-2s2 -4s + 10, 2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" =...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
SIII 4. Evaluate 3 (cos 30°)2 +2 (sin 60°)2 without using a calculator. 12. Given that sin 0 =-. Show that sin (90° — O)=cos .
(2) Show that f(t) - e3t cos(3t) is of exponential order. (3) Explain why gt)+sin is not of exponential order.
Perform the indicated operation and write the answer in the form a +bi, where a and b are real numbers. 28) (6-5i)(7 +3i) A) -15;2 - 171 +42 B) 57 - 171 C) 27 - 531 D) 57 +171 Write the quotient in the form a +bi. 9 +41 29) 2-4i B) -1.4, C) -1 5 Use De Moivre's theorem to simplify the expression. Write the answer in a +bi form. 30) (3 (cos 120° + i sin 120°))4 A)...
I know the answer is D, but can someone explain why its all cos and the angles as well? 30" to Fig 3-2 The components of vectors A and B are 42) 4) Ax -A sin 90° 3) A -Acos90° B -B sin60° Ay- A sin90° By B cos60 By B cos30 o) Ar -A co A cos90 By cos60
Find the exact value of the expression. sin (30) sin(90°) - cos (30) cos(90°) = Find the exact value of the expression. sin( – 45° ) sin( - 30°) = [ Write each expression as a single trigonometric function. sin(7x)cos(3x) – cos(7:c )sin(32) = Write each expression as a single trigonometric function. cos(6.c )cos(3x) - sin(62) sin(30) = Write each expression as a single trigonometric function. cos(7x)cos (4:0) + sin(78) sin(4x) =
please show all work 1: Let 0 << 27, and set A= I cos(0) co -sin(0) 1 | sin(@) cos(0) . (a) Recall that fa(4) denotes the characteristic polynomial for A. Show that faa) = (1 - cos(O))2 + sin(0). (b) Using part (a) show that A has no eigenvalues if is not equal to 0 or . [ 2 -2 0 0 1 1 -1 0 0 2: Set B= 10 0 3 -4 0 0 2 -3 (a)...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...