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Solving Complex Equations

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StarStarStarStar

z^3 = 8

StarStarStarStar

z = 2, z = -1 + i\sqrt{3}, z = -1 - i\sqrt{3}

StarStarStarStar

z^2 = -4

StarStarStarStar

z = 2i, z = -2i

StarStarStarStar

z + 1/z = 2

StarStarStarStar

z = 1

StarStarStarStar

z^4 = 16

StarStarStarStar

z = 2, z = -2, z = 2i, z = -2i

StarStarStarStar

e^z = 1

StarStarStarStar

z = 2k\pi i, k \in \mathbb{Z}

StarStarStarStar

z^2 + 4 = 0

StarStarStarStar

z = 2i, z = -2i

StarStarStarStar

z^2 + z + 1 = 0

StarStarStarStar

z = \frac{-1 + i\sqrt{3}}{2}, z = \frac{-1 - i\sqrt{3}}{2}

StarStarStarStar

e^z = i

StarStarStarStar

z = \frac{\pi}{2} + 2k\pi i, k \in \mathbb{Z}

StarStarStarStar

z^2 - 6z + 9 = 0

StarStarStarStar

z = 3

StarStarStarStar

iz + 1 = 0

StarStarStarStar

z = -\frac{1}{i} = i

StarStarStarStar

z^2 = -1

StarStarStarStar

z = i, z = -i

StarStarStarStar

z^4 = -16

StarStarStarStar

z = \sqrt[4]{16}e^{\frac{\pi i}{4}}, z = \sqrt[4]{16}e^{\frac{3\pi i}{4}}, z = \sqrt[4]{16}e^{\frac{5\pi i}{4}}, z = \sqrt[4]{16}e^{\frac{7\pi i}{4}}

StarStarStarStar

z^2 + 1 = 0

StarStarStarStar

z = i, z = -i

StarStarStarStar

z^2 = 1 - i

StarStarStarStar

z = \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}}i, z = -\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}i

StarStarStarStar

iz^2 + z - i = 0

StarStarStarStar

z = -i, z = 1

StarStarStarStar

z^5 = 32i

StarStarStarStar

z = 2e^{\frac{\pi i}{10}}, z = 2e^{\frac{3\pi i}{10}}, z = 2e^{\frac{5\pi i}{10}}, z = 2e^{\frac{7\pi i}{10}}, z = 2e^{\frac{9\pi i}{10}}

StarStarStarStar

z^4 + 4 = 0

StarStarStarStar

z = 1 + i, z = -1 - i, z = 1 - i, z = -1 + i

StarStarStarStar

e^{2z} = 4

StarStarStarStar

z = \log{2} + k\pi i, k \in \mathbb{Z}

StarStarStarStar

e^{3z} = -1

StarStarStarStar

z = \frac{1}{3}(\pi + 2k\pi i), k \in \mathbb{Z}

StarStarStarStar

z^2 = 8 \times (1 + i)

StarStarStarStar

z = 2 + 2i, z = -2 - 2i

StarStarStarStar

z^3 = i

StarStarStarStar

z = e^{\frac{\pi i}{6}}, z = e^{\frac{5\pi i}{6}}, z = e^{\frac{3\pi i}{2}}

StarStarStarStar

z^3 = -27

StarStarStarStar

z = -3, z = 3e^{\frac{\pi i}{3}}, z = 3e^{\frac{5\pi i}{3}}

StarStarStarStar

z^2 - 2z + 2 = 0

StarStarStarStar

z = 1 + i, z = 1 - i

StarStarStarStar

e^{2z} + 1 = 0

StarStarStarStar

z = i\frac{\pi}{2} + k\pi i, k \in \mathbb{Z}

StarStarStarStar

e^{iz} = 1

StarStarStarStar

z = 2k\pi, k \in \mathbb{Z}

StarStarStarStar

z^8 = 256

StarStarStarStar

z = 2, z = 2e^{\frac{\pi i}{4}}, z = 2e^{\frac{2\pi i}{4}}, z = 2e^{\frac{3\pi i}{4}}, z = -2, z = 2e^{\frac{5\pi i}{4}}, z = 2e^{\frac{6\pi i}{4}}, z = 2e^{\frac{7\pi i}{4}}

StarStarStarStar

z^6 = 64

StarStarStarStar

z = 2, z = 2e^{\frac{\pi i}{3}}, z = 2e^{\frac{2\pi i}{3}}, z = -2, z = 2e^{\frac{4\pi i}{3}}, z = 2e^{\frac{5\pi i}{3}}

StarStarStarStar

z + \bar{z} = 4

StarStarStarStar

z = 2 + bi, b \in \mathbb{R}

StarStarStarStar

e^z = -i

StarStarStarStar

z = -\frac{\pi}{2} + 2k\pi i, k \in \mathbb{Z}

StarStarStarStar

z^6 + 1 = 0

StarStarStarStar

z = e^{\frac{\pi i}{6}}, z = e^{\frac{3\pi i}{6}}, z = e^{\frac{5\pi i}{6}}, z = e^{\frac{7\pi i}{6}}, z = e^{\frac{9\pi i}{6}}, z = e^{\frac{11\pi i}{6}}

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