a) z = 3 − 4 i z=3-4i z = 3 − 4 i
∣ z ∣ = 3 2 + 4 2 = 5 |z|=\sqrt{3^2+4^2}=5 ∣ z ∣ = 3 2 + 4 2 = 5
c o s θ = 3 / 5 , s i n θ = − 4 / 5 cos\theta=3/5, sin\theta=-4/5 cos θ = 3/5 , s in θ = − 4/5
θ = − 53 ° \theta=-53\degree θ = − 53°
b) z = − 2 + i z=-2+i z = − 2 + i
∣ z ∣ = 2 2 + 1 = 5 |z|=\sqrt{2^2+1}=\sqrt{5} ∣ z ∣ = 2 2 + 1 = 5
c o s θ = − 2 / 5 , s i n θ = 1 / 5 cos\theta=-2/\sqrt{5}, sin\theta=1/\sqrt{5} cos θ = − 2/ 5 , s in θ = 1/ 5
θ = 153 ° \theta=153\degree θ = 153°
d) z = 7 − i z=7-i z = 7 − i
∣ z ∣ = 7 2 + 1 = 5 2 |z|=\sqrt{7^2+1}=5\sqrt{2} ∣ z ∣ = 7 2 + 1 = 5 2
c o s θ = 7 5 2 , s i n θ = − 1 5 2 cos\theta=\frac {7}{5\sqrt{2}}, sin\theta=-\frac {1}{5\sqrt{2}} cos θ = 5 2 7 , s in θ = − 5 2 1
θ = − 1 ° \theta=-1\degree θ = − 1°
z = 1 + i z=1+i z = 1 + i
∣ z ∣ = 1 + 1 = 2 |z|=\sqrt{1+1}=\sqrt{2} ∣ z ∣ = 1 + 1 = 2
c o s θ = s i n θ = 1 / 2 cos\theta=sin\theta=1/\sqrt{2} cos θ = s in θ = 1/ 2
θ = 45 ° \theta=45\degree θ = 45°
z = − 4 − 3 i z=-4-3i z = − 4 − 3 i
∣ z ∣ = 4 2 + 3 2 = 5 |z|=\sqrt{4^2+3^2}=5 ∣ z ∣ = 4 2 + 3 2 = 5
c o s θ = − 4 / 5 , s i n θ = − 3 / 5 cos\theta=-4/5, sin\theta=-3/5 cos θ = − 4/5 , s in θ = − 3/5
θ = − 143 ° \theta=-143\degree θ = − 143°
e) z = 5 ( c o s π / 3 + i s i n π / 3 ) z=5(cos π/3 + i sin π/3) z = 5 ( cos π /3 + i s inπ /3 )
∣ z ∣ = 5 c o s 2 π / 3 + s i n 2 π / 3 = 5 |z|=5\sqrt{cos^2\pi/3+sin^2\pi/3}=5 ∣ z ∣ = 5 co s 2 π /3 + s i n 2 π /3 = 5
θ = π / 3 \theta=\pi/3 θ = π /3
f) z = c o s 2 π / 3 − i s i n 2 π / 3 z=cos 2π/3 − isin 2π/3 z = cos 2 π /3 − i s in 2 π /3
∣ z ∣ = c o s 2 2 π / 3 + s i n 2 2 π / 3 = 1 |z|=\sqrt{cos^22\pi/3+sin^22\pi/3}=1 ∣ z ∣ = co s 2 2 π /3 + s i n 2 2 π /3 = 1
θ = − 2 π / 3 \theta=-2\pi/3 θ = − 2 π /3
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