(a) Show that every straight line in the Argand diagram can be represented by an equation...

 

Transcribed Image Text:

(a) Show that every straight line in the Argand diagram can be represented by an equation of the form az + bz + c = 0 where a, b, c are (complex) constants. (Hint: Let z and 22 be two distinct point on the straight line. For every other point z on the line, the number 2 - 2 must be a real multiple of 22 - 21.) (b) Let a, b, c be nonzero constant complex numbers. Is it true that az + bz + c = 0 always represents a straight line in the Argand diagram? (a) Show that every straight line in the Argand diagram can be represented by an equation of the form az + bz + c = 0 where a, b, c are (complex) constants. (Hint: Let z and 22 be two distinct point on the straight line. For every other point z on the line, the number 2 - 2 must be a real multiple of 22 - 21.) (b) Let a, b, c be nonzero constant complex numbers. Is it true that az + bz + c = 0 always represents a straight line in the Argand diagram? (a) Show that every straight line in the Argand diagram can be represented by an equation of the form az + bz + c = 0 where a, b, c are (complex) constants. (Hint: Let z and 22 be two distinct point on the straight line. For every other point z on the line, the number 2 - 2 must be a real multiple of 22 - 21.) (b) Let a, b, c be nonzero constant complex numbers. Is it true that az + bz + c = 0 always represents a straight line in the Argand diagram?

Answer rating: 100% (QA)

a Let 21 x1 iy1 and 22 x2 iy2 be two distinct points on the straight line Then the equation of the l... View the full answer