Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=1+iz = 1 + iz=1+i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=33−3iz = 3\sqrt{3} - 3iz=33−3i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=5−5iz = 5 - 5iz=5−5i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−1+3 iz = -1 + \sqrt{3}\,iz=−1+3i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=2−23 iz = 2 - 2\sqrt{3}\,iz=2−23i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−3+3 iz = -\sqrt{3} + \sqrt{3}\,iz=−3+3i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=7+73 iz = 7 + 7\sqrt{3}\,iz=7+73i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−3−iz = -\sqrt{3} - iz=−3−i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−4+4iz = -4 + 4iz=−4+4i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−23+2iz = -2\sqrt{3} + 2iz=−23+2i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=−3−33 iz = -3 - 3\sqrt{3}\,iz=−3−33i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
Determine the quadrant and principal argument arg(z)\arg(z)arg(z) of the complex number z=3−3iz = \sqrt{3} - 3iz=3−3i, expressing the argument in radians in the interval (0,2π)(0,2\pi)(0,2π).
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Question Type 3: For a given complex number, finding the modulus
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Question Type 5: Performing addition and subtraction on complex numbers