Complex Numbers Worksheets Grade 12

1. Convert the complex number 3 + 4i to polar form (r(cosθ + isinθ)) = ?
2. An electrical engineer is analyzing an alternating current circuit with two voltage sources. The first source has a voltage of 8√3 + 8i volts, and the second source has a voltage of 4√2 - 4√2i volts. To find the total voltage in the circuit, the engineer needs to convert both complex numbers to polar form and then add them. What is the total voltage expressed in polar form (r∠θ) with θ in degrees?
3. Convert the complex number 3 - 4i to polar form (r(cosθ + isinθ)) = ?

…and 5 more problems

1. Convert the complex number -4 + 4i to polar form r(cosθ + isinθ) = ?
2. Tane is designing a suspension bridge and models the force on a support cable using the complex number 9 + 12i kilonewtons. To analyze the magnitude and direction of this force, he must convert it to polar form r(cos θ + i sin θ) with θ in degrees between 0° and 360°. What is the polar form of this force?
3. Charlotte is a robotics engineer designing a control system for an industrial arm. The position of the arm's endpoint is represented by the complex number -8 + 8√3 i centimeters relative to the base. To program the arm's movement, she needs to express this position in polar form r(cos θ + i sin θ), where θ is measured in degrees between 0° and 360°. What is the polar representation of the arm's position?

…and 4 more problems

1. Hana is a sound engineer calibrating a phase shifter for a concert's audio system. The device processes a signal represented by the complex number -7√3 + 7i. To analyze the phase shift and amplitude, she must convert this signal into polar form r(cos θ + i sin θ), where θ is in radians between 0 and 2π. What is the polar representation?
2. Convert the complex number 5 - 5√3i to polar form r(cosθ + isinθ) = ?
3. A complex number is represented on the complex plane as a vector from the origin to the point (-5, 5). Express this complex number in polar form r(cosθ + i sinθ), where r > 0 and θ is the principal argument in radians between 0 and 2π.

…and 4 more problems