Thread: Complex no. problem......

Please solve my following problems.....


a)Find the complex number z , in the form a + ib that satisfy the equation z^2 = -3 +4i



B) Give the geometrical representation of the product of the two complex numbers.



c) if zz' - 5iz = 10 - 20i , find the possible values of z.

Originally Posted by asnali

Please solve my following problems.....


a)Find the complex number z , in the form a + ib that satisfy the equation [FONT=&quot] z^2 = -3 +4i

see here

B) Give the geometrical representation of the product of the two complex numbers.

For two complex numbers and we wish to geometrically interpret .

This is probably easier to visualize if you write the complex numbers in polar form, but just to describe it to you. This is taken from Bak's Complex Analysis: "If we form a triangle with two sides given by the vectors (originating from 0 to) 1 and and then form a similar triangle with the same orientation and the vector corresponding to the vector 1, the vector which corresponds to will be ."

c) if zz' - 5iz = 10 - 20i , find the possible values of z.

write so that . recall that

Thus we have

Now expand the brackets on the left, equate coefficients and solve the resulting system of equations to find and and hence,