सिद्ध कीजिए कि:
` |(2+3i ,4),(1,2-3i)|=9`

सिद्ध कीजिए कि |vecA xx vecB|^(2) + |vecA * vecB|^(2) = (AB)^(2).

यदि triangleABC में (If इन triangleABC), a = (1)/(sqrt(6)-sqrt(2)), b = (1)/(sqrt(6)+sqrt(2)), C = 60^(@) तो सिद्ध कीजिए कि (Prove that) c = (sqrt(4))/(2) .

Express the follwing in the form of a + ib, a , b in R i=sqrt ( -1). State the value of a and b. ( - sqrt5 + 2 sqrt ( -4) ) + (1 - sqrt ( -9 ))+ (2 + 3i ) (2 - 3i )

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

Simplify [ (1)/(1 - 2i ) + (3)/( 1 + i ) ][ ( 3 + 4i )/( 2 - 4i ) ]

Simplify: [1 / (1 - 2i) + 3 / (1 + i)] [(3 + 4i) / (2 - 4i)]

Express the following in the form of a + ib, where a, b in R , i = sqrt-1 . State the value of a and b. (-sqrt(5) + 2sqrt(-4)) + (1 - (sqrt-9)) + (2 + 3i) (2 - 3i)

Express the following in the form of (a+ib), a,b in R, i= sqrt (-1) State the values of a and b: ( sqrt 5 +2 sqrt (-4) )+(1- sqrt (-9) )+(2+3i)(2-3i)

Convert each of the following in the form of (a + i b) : (i) 3(1+i)-2(2+3i) (ii) (1)/(4-5i) (iii) (1-2i)^(-2) (iv) (2-3i)/(3+5i) (v) [(1)/(1-2i)+(3)/(1+i)][(3+4i)/(2-4i)]

i^(9)+i^(10)-3i^(12)=-4