Question Detail

MTH 101 MTH 101 Past Questions Objective Question
Take CBT

Question

Determine the square root of \( z = 4(\cos 70^\circ + i \sin 70^\circ) \)
Options
A \( z^2 = 8(\cos 70^\circ + i \sin 70^\circ)^2 \)
B \( z = 16(\cos 70^\circ + i \sin 70^\circ) \)
C \( \sqrt{z} = 2(\cos 35^\circ + i \sin 35^\circ) \)
Correct Answer
D \( 2z = 8(\cos 70^\circ + i \sin 70^\circ)^2 \)
Correct Answer

Option C is the correct answer.

Detailed Explanation

The square root of a complex number in polar form is given by √z = √r (cos(θ/2) + i sin(θ/2)). Here, √r = √4 = 2, and θ/2 = 35°. So √z = 2(cos 35° + i sin 35°).

Hint

To find the square root, take the square root of the modulus and halve the argument: √(r(cosθ + i sinθ)) = √r(cos(θ/2) + i sin(θ/2)).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 524 of 696
Previous Course Details Next