Write the complex number in polar form with argument 𝜃 between 0 and 2𝜋.

Question

1. -9square2-9square2 2. -square3-i

Answer 1

-9 square root of 2 sounds like the hypotenuse of a reference angle of 45 degrees, with two sides one length 9 and the other length -9

that would place it in either quadrant II or IV. the angle would be either 135 or 315, 3pi/4 or 7pi/4

real numbers on the x axis, imaginary on the y axis

that would be either -9 + 9i or 9-9i

(9sqr2, 3pi/4) or (9sqr2, 7pi/4)

or (-9sqr2, 3pi/4) or (-9sqr2, 7pi/4)

or just (+9sqr2, 3pin/4) where n = 1 or 2

or just (+ 9sqr2, 3pi/4)

-sqr3 - i is in quadrant III with sides -1 and -sqr3. hypotenuse = square root of (-1)^2 + (-sqr3)^2 = sqr(4) = 2

= (2, 7pi/6)