Question

Convert the complex number 3 - 3i into its polar representation. a. 3(cos(60degrees) + isin(60degrees)) b. 3√2(cos(135degrees) + isin(135degrees)) c. √3(cos(225degrees) + isin(225degrees)) d. 3√(cos(315degrees) + isin(315degrees))

Answer 1

Polar representation of any complex number is given by

\[z = |z| (\cos (\theta)+i \sin(\theta))\]

Answer 2

For a complex number a+bi
the magnitude is found by sqrt(a^2 +b^2)
the angle is found by tan(theta) = b/a

Answer 3

As dumbcow said above

|z|-->Magnitude
θ-->angle

Answer 4

so the answer is b. 3√2(cos(135degrees) + isin(135degrees))?