Complex Polar Operations Worksheets Grade 12

1. A complex number is represented in the complex plane with magnitude 8 and an angle of 45° from the positive real axis. This number is then multiplied by another complex number with magnitude 2 and an angle of 15°. What is the magnitude and angle (in degrees) of the resulting product? Express your answer in the form: magnitude, angle.
2. On an Argand diagram, Noah plots a complex number z₁ with a modulus of 9 and an argument of 135°. He then plots another complex number z₂ with a modulus of 3 and an argument of 45°. If Noah multiplies z₁ by z₂, what is the modulus and argument (in degrees) of the resulting complex number? Express your answer as: modulus, argument.
3. On an Argand diagram, Hana draws two complex numbers. The first number, z₁, has a modulus of 6 and an argument of 210°. The second number, z₂, has a modulus of 4 and an argument of 135°. Hana multiplies z₁ by z₂ and then divides the result by a third complex number, z₃, which has a modulus of 3 and an argument of 60°. What is the modulus and argument (in degrees) of the final complex number? Express your answer in the form: modulus, argument.

…and 3 more problems

1. A complex number is represented on the complex plane with a magnitude of 8 units and an angle of 150° from the positive real axis. If this number is multiplied by another complex number with magnitude 2 and angle 60°, what is the resulting complex number in polar form (r, θ)?
2. Dr. Chen is analyzing quantum states in a physics experiment. The first quantum state is represented by the complex number 5(cos(π/4) + i sin(π/4)) and the second state is 3(cos(π/12) + i sin(π/12)). To determine their entanglement probability, she needs to multiply these complex numbers in polar form. What is the product in polar form?
3. A complex number is represented on the Argand diagram as a point with coordinates (3, 4). Convert this complex number to polar form (r, θ), where r is the magnitude and θ is the principal argument in radians.

…and 4 more problems

1. Mason is an electrical engineer designing a power distribution network for a large industrial facility. He needs to analyze the combined effect of two alternating current sources connected in series. The first source has a voltage represented by the complex number 8∠75° volts, and the second source has a voltage represented by the complex number 9∠-20° volts. To determine the total voltage output of the series combination, Mason must multiply these complex numbers in polar form. What is the product in polar form (r∠θ) with the angle in degrees?
2. On an Argand diagram, Noah represents a complex number z₁ with a vector of magnitude 12 units making an angle of 210° with the positive real axis. He then multiplies z₁ by another complex number z₂, represented by a vector of magnitude 4 units making an angle of 135° with the positive real axis. What is the magnitude and angle (in degrees) of the resulting product vector? Express your answer in the form: magnitude, angle.
3. A complex number is represented in the complex plane with modulus 8 and argument 2π/3 radians. If this number is multiplied by another complex number with modulus 2 and argument π/6 radians, what is the modulus and argument of the resulting complex number? Express your answer in the form 'modulus: [value], argument: [value] radians'.

…and 3 more problems