Final answer:
To write the complex number z = 4 - 3i in trigonometric form, we can use the formulas to find its magnitude and argument. The magnitude of z is 5 and the argument is -36.87°. Therefore, z can be written as 5(cos(-36.87°) + i*sin(-36.87°)).
Step-by-step explanation:
To write the complex number z = 4 - 3i in trigonometric form, we need to find the magnitude and argument of the complex number.
The magnitude (or modulus) of the complex number is given by the formula: |z| = sqrt(a^2 + b^2), where a and b are the real and imaginary parts of the complex number. For z = 4 - 3i, the magnitude is calculated as: |z| = sqrt(4^2 + (-3)^2) = sqrt(16 + 9) = sqrt(25) = 5.
The argument (or angle) of the complex number is determined using the formula: arg(z) = atan(b/a), where a and b are the real and imaginary parts of the complex number. For z = 4 - 3i, the argument is calculated as: arg(z) = atan((-3)/4) = atan(-0.75) = -36.87° (rounded to two decimal places).
Therefore, the complex number z = 4 - 3i can be written in trigonometric form as: 5(cos(-36.87°) + i*sin(-36.87°)).