Complex
i^(22)=
-1
sqrt(-48)=
4isqrt(3)
i^(53)=
i
sqrt(-56)=
2isqrt(14)
i^(2020)=
1
isqrt(-27)=
-3sqrt(3)
i^(12345678}=
-1
(2+3i)(1-i)=
5+i
(1+5i)(4-2i)=
14+18i
Factor x^3+36x
x(x+6i)(x-6i)
Solve for m and n
2(m+ni)-12i=ni-8
m=-4, \ n=12
Factor
x^2+121
(x+11i)(x-11i)
Solve for x and y
3x-2i=18-2yi-6x
x=2, \ y=1
Factor
x^3+4x
x(x+2i)(x-2i)
|-5-2i|=
sqrt(29)
Solve 2x^2+49=0
x=pm(7isqrt(2))/(2)
|6-3i|=
3sqrt(5)
Solve 5x^2+4=0
x=pm(2isqrt(5))/(5)
|2+4i|=
2sqrt(5)
(sqrt(-18))/(isqrt(2))=
3
(8+sqrt(-4) )(-2+sqrt(-9))=
-22+20i
(6i)/(1+i)
3+3i
(1+i)/(i^2)+(1+i)/(i^3)
-2
Solve
x^4+35x^2-36=0
x=pm1,\ x=pm6i
Solve
x^4-24x^2-25=0
x=pmi, \ x=pm5
(1+i)/(1-i)=
i
(2-i)/i+(2-i)/(i^2)
-3-i
1/(2-3i)
2/(13)+3/(13)i
(4+2i)/(2+4i)=
4/5-3/5i
(1/2i-1/2)^8=
1/(16)
(i^4+2i^3+3i^2+4i+5)/(i^5)=
2-3i
(2i-2)^(6)=
512i
(2+2i)/(1+2i)
6/5-2/5i
(5i^5+4i^4+3i^3+2i^2)/i
2-2i
(1+i)^(16)=
256