Question

A complex number -33 - j32 can be expressed in exponential form as A * exp(jB), where A is the magnitude and B is the angle of the complex number.

Answer 1

To express the complex number -33 - j32 in exponential form, use Euler's formula and find its magnitude and angle.

Step-by-step explanation:

Solution:

To express the complex number -33 - j32 in exponential form, we can use Euler's formula which states that e^(ix) = cos(x) + i sin(x). The magnitude A is found by taking the square root of the sum of the squares of the real and imaginary parts: A = sqrt((-33)^2 + (-32)^2) = sqrt(1089 + 1024) = sqrt(2113) ≈ 45.98. The angle B can be found using the inverse tangent function: B = atan(-32 / -33) ≈ 0.758 radians or 43.44 degrees. Therefore, the complex number -33 - j32 in exponential form is approximately 45.98 * e^(i0.758) or 45.98 * cos(0.758) + i * 45.98 * sin(0.758).