Question

I need help where to start on this question i think what confuses me from the get go is the exponents, the question ask to express in trignometric form.

Z=(sqrt 3 - i)^2/(sqrt 2 - i sqrt 2)^6

Answer 1

Let z = a + bi.
Then r = sqrt(a^2+b^2) = sqrt(1^2+(sqrt3)^2) = 2
and phi = arctan(b/a) = arctan(sqrt3) = 60° = pi/3

So you have
polar form: z = r*e^(i*phi) = 2*e^(i*pi/3)
and trigonometric form:
z = r*(cos(phi) + i*sin(phi))
= 2*(cos(pi/3) + i*sin(pi/3))

Answer 2

that would be for the numerator part where you changed it into trig form, but afterwards would i apply z1//z2 quotient formula

Answer 3

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