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Simplify the expression to a + bi form:Answer:
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Q. Simplify the expression to a + bi form:Answer:
- Use Distributive Property: To simplify the expression , we need to use the distributive property (also known as the FOIL method for binomials), which states that for any complex numbers , , , and , . Let's multiply the real parts and the imaginary parts accordingly.
- Multiply Real Parts: First, we multiply the real parts: .
- Multiply Real and Imaginary: Next, we multiply the real part of the first complex number by the imaginary part of the second complex number: .
- Multiply Imaginary and Real: Then, we multiply the imaginary part of the first complex number by the real part of the second complex number: .
- Multiply Imaginary Parts: Finally, we multiply the imaginary parts: . Since , this becomes .
- Combine All Parts: Now, we combine all the parts: real part , imaginary parts , and the result of the multiplication of the imaginary parts .So, .
- Combine Like Terms: Combine like terms: is the real part, and is the imaginary part.The real part is .The imaginary part is .
- Get Final Expression: Putting it all together, we get the expression in form: .
