Draw the triangle with vertices 21 = 2 – 4i, z2 = -5 – 4i and z2 = plane and also find the area of the triangle. -6+ 8i on a complex %3D

Q: Simplify the complex number (Z^3) * ?and find the Re(z) & Im(z)

A: From De Moivre's Theorem we have,  Let z=rcosθ +isinθis a complex number in polar form. If n is a…

Q: (1 + i) 201.

A: Now…

Q: Extract the square root of the complex number 8-6i.

A: We have to find the square root of the complex number 8-6i.

Q: Solve 3x3 + 2x - 1 = 8x2 - 4 in the complex numbersystem.

A: The given equation is 3x3+2x-1=8x2-4. Solve this equation as follows.…

Q: Find the imaginary part of 2 to the power i+3

A: 2i+3 = 23•2i = 8•2i  Now, 2i = ei•ln(2) = cos{ln(2)} + i•sin{ln(2)}

Q: Find the value of y in the complex equation (2x-3yi(3 + 4i) 78-21i O5 -3 03 -4

A: Given, (2x-3yi)(3+4i)=78-21i Expanding the LHS⇒ (2x-3yi)(3+4i)=6x+8xi-9yi-12yi2…

Q: Express the result in trigonometry and rectangular form (1 + 2i)4 44. (1 – 2i)?

A: