How do you multiply two complex numbers in trigonometric form?

How do you multiply two complex numbers in trigonometric form?

• A. z1z2 = r1r2(cos(x - y) + isin(x - y))
• B. z1z2 = r1r2(cos(x + y) + isin(x + y))
• C. z1z2 = (r1 + r2)(cos(x + y) + isin(x + y))
• D. z1z2 = r1r2(cos(x) + isin(y))

Answer: (B)

When multiplying two complex numbers in trigonometric form, we use the concept of their magnitudes and angles. The general form of a complex number in trigonometric (or polar) form is expressed as \( r(\cos(x) + i\sin(x)) \), where \( r \) is the magnitude and \( x \) is the argument (angle) of the complex number. To multiply two complex numbers \( z_1 \) and \( z_2 \), we combine their magnitudes and add their angles. Specifically, if we have: \[ z_1 = r_1 (\cos(x_1) + i \sin(x_1)) \] \[ z_2 = r_2 (\cos(x_2) + i \sin(x_2)) \] The product \( z_1 z_2 \) can be calculated as follows: 1. The magnitudes multiply: \( r_1 \cdot r_2 \). 2. The angles add: \( x_1 + x_2 \). Therefore, the product can be expressed as: \[ z_1 z_2 = r_1 r_2 \left( \cos(x_1 + x_2) +

When multiplying two complex numbers in trigonometric form, we use the concept of their magnitudes and angles. The general form of a complex number in trigonometric (or polar) form is expressed as ( r(\cos(x) + i\sin(x)) ), where ( r ) is the magnitude and ( x ) is the argument (angle) of the complex number.

To multiply two complex numbers ( z_1 ) and ( z_2 ), we combine their magnitudes and add their angles. Specifically, if we have:

[ z_1 = r_1 (\cos(x_1) + i \sin(x_1)) ]

[ z_2 = r_2 (\cos(x_2) + i \sin(x_2)) ]

The product ( z_1 z_2 ) can be calculated as follows:

1. The magnitudes multiply: ( r_1 \cdot r_2 ).

2. The angles add: ( x_1 + x_2 ).

Therefore, the product can be expressed as:

[ z_1 z_2 = r_1 r_2 \left( \cos(x_1 + x_2) +