Basics of complex numbers

complex numbers- have a real and imaginary numbers

%%√-1=i%%

%%-1=i^2%%= i*i= √-1*√-1= -1

%%-i=i^3%% =i^2*i

%%1=i^4%% = i^2i^2= -1-1= 1

conjugate- real stays the same and change the imaginary size

@@simplify √-18@@

• i√18
• i√9*2
• $3i√2$

@@-10x+12i=20+3yi@@

• -10x=20
    * $x=-2$
• 12i+3yi
    * $y=4$

@@(6-i)+(7+3i)@@

• 6-i+7+3i
• 6+7-i+3i
• $13+2i$

@@(3-2i)(4+i)@@

• 12+3i-8i-2i^2
• 12-5i-2(-1)
• 12-5i+2
• $14-5i$

@@1-i@@

• multiply by the conjugate
• (1-i)(1+i)
• 1 -~~i+ i~~ -i^2
• 1-(-1)
• 1+1
• $2$

@@(X^2) -4= -11@@

• x^2= -7
• √x^2= √-7
• $x= i√7$