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Find the midpoint
m of
z_(1)=(7+8i) and
z_(2)=(8-7i).
Express your answer in rectangular form.

m=◻

Find the midpoint $m$ of $z_{1}=(7+8 i)$ and $z_{2}=(8-7 i)$ . $\newline$ Express your answer in rectangular form. $\newline$ $m=\square$

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Find the midpoint

m

of

z_{1}=(7+8 i)

and

z_{2}=(8-7 i)

.

\newline

Express your answer in rectangular form.

\newline

m=\square

Concept of finding midpoint: Understand the concept of finding the midpoint of two complex numbers. The midpoint $m$ of two complex numbers $z_1$ and $z_2$ is given by the average of their real parts and the average of their imaginary parts. m = \frac{{\text{Re}(z_1) + \text{Re}(z_2)}}{\(2\)} + \frac{{\text{Im}(z_1) + \text{Im}(z_2)}}{\(2\)}i
Identifying real and imaginary parts: Identify the real and imaginary parts of \(z_1 and $z_2$ . For $z_1 = 7 + 8i$ , the real part $\text{Re}(z_1)$ is $7$ and the imaginary part $\text{Im}(z_1)$ is $8$ . For $z_2 = 8 - 7i$ , the real part $\text{Re}(z_2)$ is $8$ and the imaginary part $z_2$ $0$ is $z_2$ $1$ .
Calculating average of real parts: Calculate the average of the real parts of $z_1$ and $z_2$ . $\frac{\text{Re}(z_1) + \text{Re}(z_2)}{2} = \frac{7 + 8}{2} = \frac{15}{2} = 7.5$
Calculating average of imaginary parts: Calculate the average of the imaginary parts of $z_1$ and $z_2$ . $\frac{\text{Im}(z_1) + \text{Im}(z_2)}{2} = \frac{8 - 7}{2} = \frac{1}{2} = 0.5$
Combining averages to find midpoint: Combine the averages to find the midpoint $m$ in rectangular form. $m = 7.5 + 0.5i$

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