Complex Number in the Standard Form

We will learn how to expand a complex in the standard form a + ib.

The following steps will help us to express a complex number in the standard form:

Step I: Obtain the complex number in the form a+ibc+id by using fundamental operations of addition, subtraction and multiplication.

Step II: Multiply the numerator and denominator by the conjugate of the denominator.


Solved examples on complex number in the standard form:

1. Express 123i in the standard form a + ib.

Solution:

We have 123i

Now multiply the numerator and denominator by the conjugate of the denominator i.e., (2 + 3i), we get

= 123i × 2+3i2+3i

= 2+3i2232i2

= 2+3i4+9

= 2+3i13

= 213 + 313i, which is the required answer in a + ib form.


2. Express the complex number 1i1+i in the standard form a + ib.

Solution:

We have 1i1+i

Now multiply the numerator and denominator by the conjugate of the denominator i.e., (1 - i), we get

= 1i1+i × 1i1i

= (1i)212i2

= 12i+i21+1

= 12i12

= 2i2

= - i

= 0 + (- i), which is the required answer in a + ib form.


3. Perform the indicated operation and find the result in the form a + ib.

349236

Solution:

349236

= 37i26i

Now multiply the numerator and denominator by the conjugate of the denominator i.e., (2 + 6i), we get

= 37i26i × 2+6i2+6i

= (37i)(2+6i)2262i2

= 6+18i14i42i24+36

= 6+4i+4240

= 48+4i40

= 4840 + 440i,

= 65 + 110i, which is the required answer in a + ib form.




11 and 12 Grade Math 

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