HallsofIvy said:Your main problem is that [itex]arctan(-1)[/itex] is NOT [itex]5\pi/6[/itex]!
Calculate that again.
NewtonianAlch said:Well, yes (3pi)/4 is the angle you're looking for since this is in the second quadrant.
You have got |z|, and now you have the angle.
Put it into exponential form to the power of 1002, and simplify it to get the angle in terms of a principal argument.
charmedbeauty said:Ok so now I have 1^1002*(cos 3Pi/4+isin3Pi/4)
= 1*(0)=0 how do they get the minus i?
NewtonianAlch said:How did you get 0 for (cos 3Pi/4 + isin 3Pi/4) ?
Also, you have forgotten to raise that to the power.
charmedbeauty said:isnt cos 3pi/4=-0.7...
and sin 3pi/4=0.7...
Polar and cartesian forms are two ways of representing complex numbers. In polar form, a complex number is expressed in terms of its magnitude (or absolute value) and angle, while in cartesian form, it is expressed in terms of its real and imaginary parts.
To convert a complex number from cartesian to polar form, you can use the following formula: r = √(a^2 + b^2) and θ = tan^-1(b/a), where a is the real part and b is the imaginary part of the complex number.
To convert a complex number from polar to cartesian form, you can use the following formula: a = r cos(θ) and b = r sin(θ), where r is the magnitude and θ is the angle of the complex number.
Yes, a complex number can have an infinite number of polar forms, since the angle (θ) can be expressed in multiple ways (e.g. in degrees or radians).
Polar and cartesian forms are important in science because they allow us to easily perform mathematical operations on complex numbers, which are often used to represent physical quantities in fields such as physics, engineering, and mathematics.