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10 cards from this deck
Magnitude (modulus) and angle (argument) in the plane.
z=r(cosθ+isinθ)z=r(\cos\theta+i \sin\theta)z=r(cosθ+isinθ), where rrr is the modulus.
r=∣z∣=a2+b2r=|z|=\sqrt{a^2+b^2}r=∣z∣=a2+b2 for z=a+biz=a+biz=a+bi.
θ=tan−1(∣b∣/∣a∣)\theta=\tan^{-1}(|b|/|a|)θ=tan−1(∣b∣/∣a∣) for z=a+biz=a+biz=a+bi.
z=13(cos0.983+isin0.983)z=\sqrt{13}(\cos 0.983+i \sin 0.983)z=13(cos0.983+isin0.983).
r=9+3=12=23r=\sqrt{9+3}=\sqrt{12}=2\sqrt{3}r=9+3=12=23.
r=2r = 2r=2, the modulus of the complex number.
Modulus is 9+3=12=23\sqrt{9 + 3} = \sqrt{12} = 2\sqrt{3}9+3=12=23.
Depends on quadrant; specific calculations needed.
θ=180°−A\theta=180°-Aθ=180°−A or θ=π−A\theta=\pi-Aθ=π−A in radians.
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