Question

Z=3(cos 80° i sin 80°), w=4(cos 50° i sin 50°), find z/w

Answer 1

To find z/w, we need to divide z by w. First, convert z and w to rectangular form. Then, use the complex division formula to simplify the expression.

Step-by-step explanation:

To find z/w, we need to divide z by w. Let's first convert z and w to rectangular form using Euler's formula:

z = 3(cos(80°) + isin(80°)) = 3cos(80°) + 3isin(80°) = 3(0.1736 + i0.9848) = 0.5208 + i2.9544

w = 4(cos(50°) + isin(50°)) = 4cos(50°) + 4isin(50°) = 4(0.6428 + i0.7660) = 2.5712 + i3.064

Now, we can divide z by w:

z/w = (0.5208 + i2.9544) / (2.5712 + i3.064)

Using the complex division formula, we can simplify this expression:

z/w = [(0.5208 * 2.5712) + (2.9544 * -3.064)] / [(2.5712 * 2.5712) + (3.064 * 3.064)]

z/w = (1.3401 - 9.0431i) / (6.6097 + 9.3679)

After simplifying, we get:

z/w = 0.0866 - 0.8592i