-/1 points Given z 2-2i and w 1-3i, find each of the following. If you need t ty

Question

-/1 points Given z 2-2i and w 1-3i, find each of the following. If you need t type pi. For (c) and (d) click on the eye to check formatting. a) -= c) Izl d) arg(z) e) z+w symbolic formatting help Your work in questions) 5, 7, 8, 9, 10 wil also be submitted or saved. Submit Assignment Save Assignment Progress 1 points Find the three cube roots of each of the numbers below. Express your answers as a comma separated list (in any order) of t he form (z1,2,23) where zi, z2, zs are your roots in standard form a+bi Use exact values, not decimal approximations. Click on the eye to check formatting. (a) -8 (b) 8i

Explanation / Answer

I am solving the first question as per Chegg guidelines, post multiple question to get the rmeaining answers

Q1)

a) z(conjugate) = 2 + 2i

b) zz(conjugate) = (2+2i).(2-2i) = 4 - 4i + 4i - 4i^2 = 4 + 4 = 8

c) |z| = sqrt(zz(conjugate)) = sqrt(8) = 2*sqrt(2)

d) arg(z) = taninv(-2/2) = taninv(-1) = -pi/4

e) z + w = (2-2i) + (1-3i) = (2+1) + i(-2-3) = 3 - 5i

f) zw = (2-2i).(1-3i) = 2 - 6i - 2i + 6i^2 = -4 - 8i

g) z/w = (2-2i)/(1-3i) * (1+3i)/(1+3i) = 1/10 * [2 + 6i - 2i - 6i^2] = 1/10 * [8 + 4i] = 4/5 + 2/5i

h) w/z = (1-3i)/(2-2i) * (2+2i)/(2+2i) = 1/8 * [2 + 2i - 6i - 6i^2] = 1/8 * [8-4i] = 1 - 1/2i

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