
How do you graph in the complex plane?
Answer
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Hint: In order to solve this question, we identify our real number part and imaginary number part and then plot it accordingly on the graph. The x-axis represents the real numbers while the y-axis represents the imaginary numbers.
Complete step-by-step solution:
The given number is . This is a mixed number where there are two parts- a complex number and a real number.
Now, we need to plot the given equation on the complex plane. A complex plane is nothing but a Cartesian system containing the standard two axes which is the x-axis and the y-axis. The x- axis represents the real numbers while y-axis represents the imaginary numbers.
Our given number is , represents the real number while is an imaginary number.
Thus our coordinates are: where x-coordinate represents the real part and y-coordinate represents the imaginary part.
Plotting this on the graph, we get:
Here point A represents our required coordinate.
Note: A complex number is a number that can be represented as , where a and b are real numbers, and represents the imaginary unit, satisfying the equation . Because no real number satisfies the equation, therefore is called an imaginary number. Some properties of complex numbers are:
When a, b, c and d are real numbers and a+ b=c+ d, then a=c and b=d
The sum of two conjugate complex numbers is real. For example, if we have a number as , where and are real numbers, and the conjugate number , then the sum of is a real number.
The product of two conjugate complex numbers is real.
Complete step-by-step solution:
The given number is
Now, we need to plot the given equation on the complex plane. A complex plane is nothing but a Cartesian system containing the standard two axes which is the x-axis and the y-axis. The x- axis represents the real numbers while y-axis represents the imaginary numbers.
Our given number is
Thus our coordinates are:
Plotting this on the graph, we get:
Here point A represents our required coordinate.

Note: A complex number is a number that can be represented as
When a, b, c and d are real numbers and a+
The sum of two conjugate complex numbers is real. For example, if we have a number as
The product of two conjugate complex numbers is real.
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