178k views
4 votes
Write each of the following numbers in the form a+bi. (a) exp(2+iπ/4)

User Nissar
by
8.5k points

1 Answer

4 votes

Final Answer:

The number exp(2+iπ/4) can be expressed in the form a+bi as √2 + √2i/2.

Step-by-step explanation:

To express exp(2+iπ/4) in the form a+bi, we can use Euler's formula: exp(ix) = cos(x) + i*sin(x). In this case, we have exp(2+iπ/4). Breaking it down, we get exp(2) * exp(iπ/4). The real part, exp(2), is a constant, and the imaginary part, exp(iπ/4), can be expressed using Euler's formula as cos(π/4) + i*sin(π/4), which simplifies to √2/2 + √2/2i. Multiplying the real part by the constant, we get √2 * √2/2 = √2. Therefore, the final expression is √2 + √2i/2.

In summary, the complex number exp(2+iπ/4) can be written as √2 + √2i/2 in the form a+bi. This representation is derived by utilizing Euler's formula to break down the exponential expression into its real and imaginary components, followed by simplifying the imaginary part to express it in the desired form. The result, √2 + √2i/2, accurately represents the given complex number in the specified form.

User Joseph Gabriel
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories