Question

Given z1 = -3


`√(3)`
 + 3i and z2 = 6cos150° + 6isin150°, use complete sentences to explain why z1 = z2. Explain the steps of your work for full credit.


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Answer 1

See explanation

Explanation:

The given complex number are:

`z_1=-3√(3)+3i`

and

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

When we rewrite
`z_1=-3√(3)+3i` in complex form, we obtain;

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

where

`r=\sqrt{(-3√(3))^2+3^2 }=√(36)=6`

and

`\theta=tan^(-1)((y)/(x))`

`\implies \theta=tan^(-1)((-3√(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`