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blagie [28]
3 years ago
14

Given z1 = -3

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0

Answer:

See explanation

Step-by-step explanation:

The given complex number are:

z_1=-3\sqrt{3}+3i

and

z_2=6\cos 150\degree+6i\sin 150\degree

When we rewrite z_1=-3\sqrt{3}+3i in complex form, we obtain;

z_1=r(\cos \theta+i\sin \theta)

where

r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6

and

\theta=tan^{-1}(\frac{y}{x})

\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree

Hence,

z_1=6(\cos 150\degree+i\sin 150\degree)

z_1=6\cos 150\degree+6i\sin 150\degree

Hence

z_1=z_2

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Step-by-step explanation:

Qaudratics are in the form ax^2 + bx+ c

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Now, let's arrange this equation in this form:

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We need to know the discriminant to know nature of roots. The discriminant is:

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