HOW is anybody supposed to find the answer to this pre calc question???? Express the complex number in trigonometric form. -2 How am i supposed to do anything with that number? These are my choices, but I am completely lost! : 2(cos 90° + i sin 90°) 2(cos 0° + i sin 0°) 2(cos 180° + i sin 180°) 2(cos 270° + i sin 270°)

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HOW is anybody supposed to find the answer to this pre calc question???? Express the complex number in trigonometric form. -2 How am i supposed to do anything with that number? These are my choices, but I am completely lost! : 2(cos 90° + i sin 90°) 2(cos 0° + i sin 0°) 2(cos 180° + i sin 180°) 2(cos 270° + i sin 270°)

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z = |z|(cos Θ + i sin Θ) For yours z = -2 + 0i, so |z| = 2. The real part is the horizontal axis, so Θ = 0°
you could check the answer choices, which would be one way
not to disagree with @peachpi but for \(-2\) you would have \(\theta=\pi\) or if you are working in degrees for some unknown reason \(\theta=180^\circ\)

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What is that formula called? @peachpi
oh yeah. forgot about the negative
it is not a formula, it is an equality between numbers \[2(\cos(180)+i\sin(180))=2\times (-1+0)=-2\]
Ah, okay. Im getting 2(cos 0° + i sin 0°) as my answer
but that cannot be correct since \(\cos(0)=1\) not \(-1\)
Im still a bit confused on the process of getting to my answer...
it is an equality between two numbers you have \(-2\) right?
the absolute value of \(-2\) is \(2\)
therefore it will be \[2(\cos(\theta)+i\sin(\theta))=-2\] which is only possible if \(\sin(\theta)=0\) since \(-2\) has no \(i\) in it and if \(\cos(\theta)=-1\) since \(2\times -1=-2\)
so one possible value of \(\theta\) is \(180\) as \(\cos(180)=-1\) and \(\sin(180)=0\)

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