\( 182322 \angle 63 \)

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The notation \( 182322 \angle 63 \) typically represents a complex number in polar form, where \( 182322 \) is the magnitude (or modulus) and \( 63 \) is the angle (or argument) in degrees. To convert this polar form to rectangular (Cartesian) form, we can use the following formulas: \[ x = r \cos(\theta) \] \[ y = r \sin(\theta) \] where: - \( r \) is the magnitude (182322), - \( \theta \) is the angle in radians. First, we need to convert the angle from degrees to radians: \[ \theta = 63^\circ \times \frac{\pi}{180^\circ} \approx 1.09956 \text{ radians} \] Now we can calculate \( x \) and \( y \): \[ x = 182322 \cos(63^\circ) \approx 182322 \times 0.4488 \approx 81763.78 \] \[ y = 182322 \sin(63^\circ) \approx 182322 \times 0.7880 \approx 143,000.00 \] Thus, the rectangular form of the complex number is approximately: \[ x + yi \approx 81763.78 + 143000.00i \] So, \( 182322 \angle 63^\circ \) in rectangular form is approximately: \[ 81763.78 + 143000.00i \]