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  • 2 years ago

Express the complex number in trigonometric form. -4

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  1. Azteck
    • 2 years ago
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    The standard form for a complex number is: \[a+ib\] or \[x+iy\] where: "a" and "x" are the real parts of the complex number, and; "b" and "y" being the imaginary part of the complex number. when you want to find the trigonometric form you're looking for the mod-arg form: \[Rcis\theta=R(\cos\theta + i\sin\theta)\] Where R is the modulus of the complex number; "cos(theta)" being the real part; "sin(theta)" being the imaginary part, and; "theta" being the argument of the complex number. For your example being -4. We should find the the modulus first using the Phythagorean formula: \[R=\sqrt{a^2+b^2}\] \[=\sqrt{(-4)^2+0^2}\] \[=\sqrt{16}\] \[=4\] Now you should find the angle or argument of -4. Use this graph to find the angle you're looking for: |dw:1371802552197:dw| Then you can connect all the information you gathered- the modulus (the distance) and the argument (the angle); so now you can put all that into the mod-arg form given to you by me.

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