Question

Let
z1 = 3+2j
z2 = 4+5j

Calculate z1*z2 and state Re(z1*z2) & Im(z1*z2)

Answer 1

Answer on Question #51656 – Math – Complex Analysis

Let

$$z _ {1} = 3 + 2 j$$ $$z _ {2} = 4 + 5 j$$

Calculate $z_{1} * z_{2}$ and state $Re(z_{1} * z_{2}) \& Im(z_{1} * z_{2})$.

Solution:

The product of complex numbers $z_{1}$ and $z_{2}$ is defined to be the number

$$(a + b j) (c + d j) = (a c - b d) + (b c + a d) j,$$ $$\begin{array}{l} z _ {1} * z _ {2} = (3 + 2 j) (4 + 5 j) = (3 \cdot 4 - 2 \cdot 5) + (3 \cdot 5 + 2 \cdot 4) j = (1 2 - 1 0) + (8 + 1 5) j \\ = 2 + 2 3 j \\ \end{array}$$

The real part of complex number $z = a + bi$ is $Re(z) = a$,

$$R e (z _ {1} * z _ {2}) = R e (2 + 2 3 j) = 2.$$

The imaginary part of complex number $z = a + bi$ is $Im(z) = b$,

$$I m (z _ {1} * z _ {2}) = I m (2 + 2 3 j) = 2 3$$

Answer:

$$z _ {1} * z _ {2} = 2 + 2 3 j$$ $$R e (z _ {1} * z _ {2}) = 2$$ $$I m (z _ {1} * z _ {2}) = 2 3$$

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