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Perform the indicated operations on the following complex numbers and express the answer in standard form.
- 8i(2i - 9)
Simplify the following expression and express the answer in standard form, if necessary.
(3 + 7i)/(6 - 2i)
Plot the given complex number on a graph. Express the complex number in the polar form.
5 + 5i
Express the given complex number in rectangular form. Write your answer in one decimal place, if necessary.
18(cos 30° + i sin 30°)
Divide the following complex numbers (z1/z2) and express the final answer in polar form. Ensure that for the final answer, 0° ≤ θ ≤ 360°.
z1 = cos 65° + i sin 65°
z2 = cos 315° + i sin 315°
Multiply the following complex numbers and express the final answer in polar form.
z1 = 9(cos 35° + i sin 35°)
z2 = 7(cos 65° + i sin 65°)
Find [5(cos 75° + i sin 75°)]⁴ using DeMoivre's Theorem. Express the answer in rectangular form.
Determine all the complex fifth roots of 243(cos (5π/6) + i sin (5π/6)). Express the roots in rectangular form and round to one decimal if needed.