posted by .

How to convert into polar form?

z = 1 - i

w = 1 - √3i

The polar form expresses a complex number as:

z = |z| exp(i theta)

theta is the angle with the positive real axis.

For z = 1 - i, we have:

|z| = sqrt(2)

Then it's easy to see that you can take theta = -pi/4:

exp(-i pi/4) = cos(pi/4) - i sin(pi/4) =
1/sqrt(2) (1-i).

Then in case of

w = 1 - √3i

you have:

|w| = sqrt(4) = 2

And you easly see that theta = -pi/3

You can compute theta directly by taking arctan of imaginary part divided by the real part, but you may then need to add pi to this. If you multiply z by -1, theta changes by plus or minus pi, while the ratio stays the same.

In polar form, the first is (1/sqrt(2),-pi/4)

The second is (2,-pi/3)

## Similar Questions

1. ### precalculus

convert the equation y^2 = 2x -x^2 into polar form. convert the equation r = 2tan(theta) into rectangular form. I'm not really sure what either of these mean. I vaguely understand polar coordinates, but I'm not sure how to convert …

I don't get how to do this. I'm so lost please help me. Determine the equation of the parabola with roots 2+√3 and 2-√3, and is passing through the point (2,5) this is what i did but its the wrong answer: y= a[x + (2+√3)] …

convert the polar equation to rectangular form. 1.) r sec(theta) = 3 2.) r = 4 cos(theta) - 4 sin(theta) convert from rectangular equation to polar form. 1.) x^2 + (y-1)^2 = 1 2.) (x-1)^2 + (y+4)^2 = 17
4. ### pre calc.Math

Please help me any one of these please! Thank You to any one r=2-6 cos(θ) convert this polar coordinate equation into an equation in rectangular coordinates(x,y) given (-8,8) convert this point into polar coordinates with 6 >= …

Please show work Simplify rational 1. 4√(a^6 b^13) / 4√(a^2b) 2.√(2x^3 / 49y^4) Add or Subtract 3. x√(75xy) - √(27x^3y) Multiply 4.(√(5) - 5) (2√(5) + 2) Rationalize the denominator 5. √(25x^5 …
6. ### Math help Ms. Sue please

1. What is the simplified form of the expression?