1) Perform the operation and leave the result in trig. form.
[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]
Thanks
[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]
= (3/4)(1/2 + i (√3/2) (4) (-√2/2 + i √2/2)
= (3/4)(1/2)(1 + i √3)(4)(1/2)( -√2 + i √2)
= (3/4)(-√2 + i√2 - i √6 + √6 i^2)
= (3/4) (-√2 -√6 + i(√2-√6) ) --- in quad III
tan^-1 | √2-√6|/|-√2-√6| = 15° or π/12
but the angle is in III , so Ø = 135° or 9π/12
= (3/4)( cos 9π/12 + i sin 9π/12)
check my arithmetic, I should have written it out on paper first.
To solve this problem, we need to multiply the given complex numbers, 3/4(cos pi/3 + i sin pi/3) and 4(cos 3pi/4 + i sin 3pi/4). To multiply complex numbers in trigonometric form, we multiply the magnitudes and add the angles.
First, let's find the magnitude of both complex numbers:
Magnitude of the first complex number = 3/4
Magnitude of the second complex number = 4
Next, let's find the sum of the angles:
Angle of the first complex number = pi/3
Angle of the second complex number = 3pi/4
Sum of the angles = pi/3 + 3pi/4
Now, let's calculate the result:
Magnitude of the result = (3/4)(4) = 3
Angle of the result = pi/3 + 3pi/4
To add the angles, we need to find a common denominator, which in this case is 12. Let's convert the angles to have a common denominator:
Angle of the result = (4pi/12) + (9pi/12) = 13pi/12
Therefore, the result in trigonometric form is 3(cos 13pi/12 + i sin 13pi/12).