A   complex number   is a number which can be written as:




a
+
b
×
i


{\displaystyle a+b\times i}


(sometimes shown as:




b
+
a
×
i


{\displaystyle b+a\times i}


where   



a


{\displaystyle a}

   and   



b


{\displaystyle b}

  are real numbers,   and   



i


{\displaystyle i}

   is   √ -1 



Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part",   where the imaginary part is the number to be multiplied by 



i


{\displaystyle i}

.



Task

 Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.) 
 Print the results for each operation tested.
 Optional: Show complex conjugation.


By definition, the   complex conjugate   of




a
+
b
i


{\displaystyle a+bi}


is




a
−
b
i


{\displaystyle a-bi}





Some languages have complex number libraries available.   If your language does, show the operations.   If your language does not, also show the definition of this type.




5 LET complex=2: LET r=1: LET i=2
10 DIM a(complex): LET a(r)=1.0: LET a(i)=1.0
20 DIM b(complex): LET b(r)=PI: LET b(i)=1.2
30 DIM o(complex)
40 REM add
50 LET o(r)=a(r)+b(r)
60 LET o(i)=a(i)+b(i)
70 PRINT "Result of addition is:": GO SUB 1000
80 REM mult
90 LET o(r)=a(r)*b(r)-a(i)*b(i)
100 LET o(i)=a(i)*b(r)+a(r)*b(i)
110 PRINT "Result of multiplication is:": GO SUB 1000
120 REM neg
130 LET o(r)=-a(r)
140 LET o(i)=-a(i)
150 PRINT "Result of negation is:": GO SUB 1000
160 LET denom=a(r)^2+a(i)^2
170 LET o(r)=a(r)/denom
180 LET o(i)=-a(i)/denom
190 PRINT "Result of inversion is:": GO SUB 1000
200 STOP 
1000 IF o(i)>=0 THEN PRINT o(r);" + ";o(i);"i": RETURN 
1010 PRINT o(r);" - ";-o(i);"i": RETURN 
 