Question

Express 5×√3−5i in polar form.

A. 10∠ π/6
B. 10∠− π/6
C. 5∠ π/3
D. 5∠− π/3

Answer 1

The complex number 5×√3-5i in polar form is 10∠(-π/6), which corresponds to option B. Therefore, the polar form of this complex number is 10∠(-π/6), which corresponds to option B.

Step-by-step explanation:

The complex number 5×√3-5i in polar form is represented as r∠θ, where r is the modulus and θ is the argument of the complex number.

To find the modulus r, you calculate the square root of the sum of the squares of the real and imaginary parts: r = √((5×√3)²+(-5)²), which simplifies to r = 10.

To find the argument θ, you use the arctangent of the imaginary part over the real part: θ = atan2(-5, 5×√3), which gives θ = - π/6.

Therefore, the polar form of this complex number is 10∠(-π/6), which corresponds to option B.