Question

How do you simplify \[(8+5i)-(1+2i)\] and write the complex number in standard form ?

Answer 1

Hint: To simplify the given operation on complex numbers, firstly we should remove the complex numbers from brackets to simplify them. The next step is to write the real part and the imaginary parts of complex terms separately. Now add the real terms of the complex numbers and imaginary part of the complex numbers and present the obtained complex number in usual standard form it is \[a\]+ \[ib\] where \[a\] is the real part and \[ib\] is imaginary part.

Complete step by step solution:
Here the given problem for simplification is as follows,
\[\left( 8+5~i \right)\left( 1+2i \right)\]
Firstly we will open the complex terms from brackets,
\[\Rightarrow \]\[8+5i-1-2i\]
Now we will write the real parts and imaginary parts of complex numbers separately,
\[\Rightarrow \]\[8-1+5i-2i\]
\[\Rightarrow \] \[7+\left( 5-2 \right)i\]
Next we will perform the operation in both parts ,
\[\Rightarrow \] \[7+\left( 3 \right)i\]
At last, we will express it in standard form,
\[\Rightarrow \] \[7+3i\]
So the simplified form of given complex numbers \[(8+5i)-(1+2i)\] is \[7+3i\] which is written in standard form it is \[a+ib\] .

Note: The arithmetic operation of the complex numbers can also be solved directly without segregation of real parts and imaginary parts of complex numbers. Here it is important for us to add the real parts of one complex number with the real part of another complex number only and similarly imaginary parts of one complex number with imaginary part of another complex number only.