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Problems Algebra and arithmetic Complex numbers Cartesian form of a complex number, complex conjugate, Argand diagram, etc

14–16 2.0

Let $z = x + i y$ , $w = u + i v$ . Find a) $z + w$ ; b) $z w$ ; c) $z / w$ .

Problem #PRU-61066

Problems Algebra and arithmetic Complex numbers Cartesian form of a complex number, complex conjugate, Argand diagram, etc

14–16 2.0

Prove the equalities:

a) $\overset{―}{z + w} = \overset{―}{z} + \overset{―}{w}$ ; b) $\overset{―}{z w} = \overset{―}{z} \overset{―}{w}$ ; c) $\overset{―}{\frac{z}{w}} = \frac{\overset{―}{z}}{\overset{―}{w}}$ ; d) $| \overset{―}{z} | = | z |$ ; d) $\overset{―}{\overset{―}{z}} = z$ .

Problem #PRU-61067

Problems Algebra and arithmetic Complex numbers Cartesian form of a complex number, complex conjugate, Argand diagram, etc

14–16 2.0

Prove the equalities:

a) $z + \overset{―}{z} = 2 Re z$ ;

b) $z - \overset{―}{z} = 2 i Im z$ ;

c) $\overset{―}{z} z = | z |^{2}$ .