precalc
posted by Joshua
Suppose that z1=68i. Find:
A. The Trig Form of the complex number z1, where your theta is in degrees.
B. The Trig form of z1*z2, where
z2=5[cos(60degrees)+isin(60degrees)]
C. The Trig Form of (z1)^4

Steve
looks like z1 is in QIV, since x>0 and y<0
so, θ = 360  arctan(8/6) = 360  53.1 = 306.9°
z1 = 10 cis 306.9°
z2 = 5 cis 60°
z1*z2 = 10*5 cis (53.1+60) = 50 cis 6.9°
z1^4 = 10^4 cis 4*(53.1)
= 10000 cis 212.4°
= 10000 cis 147.6°
x = 10000 cos 147.6° = 8443
y = 10000 sin 147.6° = 5358
z1^4 = 8443 + 5359i
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