21 Let z1 = 1+ 5i and z2 = 3+2i, and let z = 22 (a) Find |z| without finding z. -1 (b) Find tan(tan-5 – tan (c) Hence write z in the form x + iy, where x and y are real. ), and hence find arg z without finding z.

Q: The indicial equation for the differential equation 2xy" + y + xy = 0 is 2c² - 1 = 0. True False

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Q: Q2/ A) Prove the identity Sin (A + B) + Sin (A - B) = 2SinA cosB %3D

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Q: (cos x +i sin a)" = cos nx +i sin na -1)

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Q: Suppose that tan(x) = 2. Compute tan (x + 1).

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Q: if sin(A)=3/5 A is in QII and tan(B)=7/24 B is in Q3 then determine tan(A+B) and cot(A+B)

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A: Derivative of one function with respect to another function. Using substitutions to find derivative.

Q: Diagonalize the following matrix, find P and D with A = PDP-¹, then compute A4 for the matrix A = 1…

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Q: expand the formula for sin(A+B)

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Q: Q2/ A) Prove the identity Sin (A + B) + Sin (A - B ) = 2SinA cosB

A: Given: sinA+B+sinA-B=2 sin A cos B To Find: To prove the given inequality.

Q: 1-tan20 = 1- 2sin?0 1+tan20

A: 1-tan2θ1+tan2θ=1-2sin2θ Formulas 1+tan2θ=sec2θ1-cos2θ=sin2θ 1secθ=cosθ