Factor over the Complex Numbers 5/2*(cos(150)+isin(150))

Problem

5/2*(cos(150)+i*sin(150))

Solution

1. Identify the complex number in polar form r*(cos(θ)+i*sin(θ)) where r=5/2 and θ=150

2. Evaluate the trigonometric functions for the angle 150 which is in the second quadrant.

3. Substitute the exact values cos(150)=−√(,3)/2 and sin(150)=1/2 into the expression.

4. Distribute the constant factor 5/2 to both the real and imaginary parts.

5. Simplify the resulting fractions to find the rectangular form a+b*i

Final Answer

5/2*(cos(150)+i*sin(150))=−(5√(,3))/4+5/4*i

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