Chapter 2: Q2P (page 63)

Express the following complex numbers in the $x + i y$ form. Try to visualize each complex number, using sketches as in the examples if necessary. $e^{i π / 2}$

Short Answer

Expert verified

The complex number $e^{i π / 2}$ in the $x + i y$ form i is and its sketch is given below.

Step by step solution

Definition of Power series.

The numbers that are presented in the form of $a + i b$ where $a, b$ , arereal numbers and $' i'$ is an imaginary number called complex numbers.

Example:.

$3 + 2 i$

Substitute the value.

It is known that $e^{i θ} = \cos θ + i \sin θ$

Substitute $θ = \frac{π}{2}$

$\begin{matrix} e^{\frac{i π}{2}} = \cos \frac{π}{2} + i \sin \frac{π}{2} \\ = 0 + i (1) \\ = i \end{matrix}$

Sketch the diagram.

Write the given expression form of $r e^{i θ}$ for that . $r = 1 and θ = \frac{π}{2}$

Draw the diagram in the coordinates.

Therefore, the general form of the given complex number is. $z = i$

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Express the following complex numbers in the $x + i y$ form. Try to visualize each complex number, using sketches as in the examples if necessary. $e^{i π / 2}$

Short Answer

Step by step solution

Definition of Power series.

Substitute the value.

Sketch the diagram.

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Express the following complex numbers in the x+iyform. Try to visualize each complex number, using sketches as in the examples if necessary.eiπ/2

Short Answer

Step by step solution

Definition of Power series.

Substitute the value.

Sketch the diagram.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Famous Physicists

Atoms and Radioactivity

Particle Model of Matter

Work Energy and Power

Scientific Method Physics

Study anywhere. Anytime. Across all devices.

Express the following complex numbers in the $x + i y$ form. Try to visualize each complex number, using sketches as in the examples if necessary. $e^{i π / 2}$