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1. (20 pts) Review the Euler's formula for complex numbers by solving several exercises below. (a) Write 1+2i, 3+3i, 4-6i, -5 using complex exponential form. (b) Write $3exp(\frac{\pi}{4}i)$, $10exp(\frac{\pi}{2}i)$, $2exp(\pi i)$ as $a+bi$ form. (c) Solve $x^3=1$, $x^4=16$ including complex number solutions. (d) Manually sketch $f(t)=2exp((\frac{\pi}{4})jt)$ (sketch all three Re vs t, Im vs t, and 3D plot; clearly show a couple of periods)

Name: 1 20 pts review the eulers formula for complex numbers by solving several exercises below a write 12i 33i 4 6i 5 using complex exponential form b write 3expfracpi4i 10expfracpi2i 2exppi i as 15971
Uploaded: 2023-05-28T02:02:10-08:00
Duration: 3 min 31 s
Channel: Madhur L
Description: 1 20 pts review the eulers formula for complex numbers by solving several exercises below a write 12i 33i 4 6i 5 using complex exponential form b write 3expfracpi4i 10expfracpi2i 2exppi i as 15971

          1. (20 pts) Review the Euler's formula for complex numbers by solving several exercises below.
(a) Write 1+2i, 3+3i, 4-6i, -5 using complex exponential form.
(b) Write $3exp(\frac{\pi}{4}i)$, $10exp(\frac{\pi}{2}i)$, $2exp(\pi i)$ as $a+bi$ form.
(c) Solve $x^3=1$, $x^4=16$ including complex number solutions.
(d) Manually sketch $f(t)=2exp((\frac{\pi}{4})jt)$ (sketch all three Re vs t, Im vs t, and 3D plot; clearly show a couple of periods)

$1 20 pts review the eulers formula for complex numbers by solving several exercises below a write 12i 33i 4 6i 5 using complex exponential form b write 3expfracpi4i 10expfracpi2i 2exppi i as 15971$

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