Question 1194520: 1. Given: Z1= 2-2i , Z2= 3i and Z3= -3+i .Find:
(c) Z1*Z3 (d) Z3xZ2 (e) the acute angle between Z1 and Z2 Found 2 solutions by prakharsingh406, ikleyn:Answer by prakharsingh406(1) (Show Source):
You can put this solution on YOUR website! z1=2-2i and z2=3i and z3= -3+1 now
c) z1*z3 = 6i-6i^2 (i^2=-1 as i =
so it will become
6i+6= 6+6i we get
Now I believe you can do d
for e
angle between z1 and z2
z1(2, -2) and z2 (0,3) on a graph
take origin as a reference point now draw on a graph
now y= 3 has 0 slope so angle 0 but 2,-2 has -pie/4 as angle= tan^-1 (-2/2)
now angle between z1 and z2 is z1-z2 is angle between them so -pie/4 -0 =-pie/4
this is the simplest method.
(c) Z1 * Z2 = (2-2i)*(-3+i) = -6 + 6i + 2i -2i^2 = -6 + 8i -2*(-1) =
= -6 + 8i + 2 = -4 + 8i.
(e) The angle (the argument) for Z1 is = -45°.
The angle (the argument) for Z2 is = 90°.
THEREFORE, the angle between Z1 and Z2 is - = .
Or, in degrees, the angle between Z1 and Z2 is 90° - (-45°) = 135°.
This answer is for minimal angle measure.
The other possible angle "between" these complex numbers is 360° - 135° = 225°,
but normally, the minimal of the two angles is considered as the answer.
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