Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Express z=−2−2iz = -2 - 2iz=−2−2i in polar and Euler form.
Convert z=1−iz = 1 - iz=1−i into polar form and Euler form, specifying θ\thetaθ explicitly.
Express z=−1+3iz = -1 + \sqrt{3}iz=−1+3i in both polar and Euler forms, with exact angles.
Express z=−4+3iz = -4 + 3iz=−4+3i in polar form and Euler form, giving the argument in the correct quadrant.
Convert the complex number 4+3i4 + 3i4+3i to polar form r(cosθ+isinθ)r(\cos\theta + i\sin\theta)r(cosθ+isinθ) and Euler form reiθre^{i\theta}reiθ.
Find the polar form and Euler form of z=−5iz = -5iz=−5i. [4]
Convert z=3−√3iz = 3 - √{3}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.
Convert z=5iz = 5iz=5i to polar and Euler forms.
Determine the modulus-argument (polar) form and exponential form of the complex number z=−3+iz = -\sqrt{3} + iz=−3+i, giving the argument θ\thetaθ in the interval −π<θ≤π-\pi < \theta \le \pi−π<θ≤π.
Express z=3+iz = \sqrt{3} + iz=3+i in polar form and Euler form, with θ\thetaθ in simplest exact form.
Convert z=22−22 iz = 2\sqrt{2} - 2\sqrt{2}\,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
