Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Convert z=5iz = 5iz=5i to polar and Euler forms.
Convert z=1−iz = 1 - iz=1−i into polar form and Euler form, specifying θ\thetaθ explicitly.
Convert the complex number 4+3i4 + 3i4+3i to polar form r (cosθ+isinθ)r\,\bigl(\cos\theta + i\sin\theta\bigr)r(cosθ+isinθ) and Euler form reiθre^{i\theta}reiθ.
Find the polar form and Euler form of z=−5iz = -5iz=−5i.
Express z=−2−2iz = -2 - 2iz=−2−2i in polar and Euler form.
Express z=−1+3 iz = -1 + \sqrt3\,iz=−1+3i in both polar and Euler forms, with exact angles.
Express z=3+iz = \sqrt3 + iz=3+i in polar form and Euler form, with θ\thetaθ in simplest exact form.
Express z=−4+3iz = -4 + 3iz=−4+3i in polar form and Euler form, giving the argument in the correct quadrant.
Convert z=3−3 iz = 3 - \sqrt3\,iz=3−3i to polar and Euler forms, giving exact values.
Find the polar and Euler forms of z=−3−3iz = -3 - 3iz=−3−3i.
Determine the polar and Euler forms of z=−3+iz = -\sqrt3 + iz=−3+i, giving θ\thetaθ in the correct quadrant.
Convert z=22−22 iz = 2\sqrt2 - 2\sqrt2\,iz=22−22i to polar and Euler forms.
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Question Type 2: Converting from Euler to polar and from polar to Cartesian