Answer:
Explanation:
To write a complex number in polar form, we need to express it as a magnitude and an angle. The magnitude of a complex number is the distance of the number from the origin (0, 0) on the complex plane, and the angle is the angle formed by the line from the origin to the number and the positive x-axis.
To find the magnitude and angle of the complex number z = -4 + 3i, we can use the following formulas:
Magnitude: |z| = sqrt(Re^2 + Im^2) = sqrt((-4)^2 + (3)^2) = sqrt(16 + 9) = sqrt(25) = 5
Angle: θ = atan(Im/Re) = atan(3/(-4)) = atan(-0.75) = -33.69 degrees
Therefore, the polar form of the complex number z = -4 + 3i is 5 * cis(-33.69 degrees). In this form, the magnitude (5) is expressed as a multiple of cis, which is short for cosine + i sine. The angle (-33.69 degrees) is given as the argument of cis, which represents the angle in radians.