Find the midpoint m of z_(1)=(5-6i) and z_(2)=(16+2i). Express your answer in rectangular form. m=

Formula for finding midpoint: To find the midpoint m of two complex numbers z1 and z2, we use the formula for the midpoint of two points in the complex plane, which is the average of the real parts and the average of the imaginary parts of the two complex numbers. Let z1 = (5 - 6i) and z2 = (16 + 2i). The real part of the midpoint m is (Re(z1) + Re(z2)) / 2 and the imaginary part of the midpoint m is (Im(z1) + Im(z2)) / 2.Given complex numbers: Calculate the real part of the midpoint m: Re(m) = (5 + 16) / 2 = 21 / 2 = 10.5Calculate real part of midpoint: Calculate the imaginary part of the midpoint m: Im(m) = (-6 + 2) / 2 = -4 / 2 = -2Calculate imaginary part of midpoint: Combine the real and imaginary parts to express the midpoint m in rectangular form: m = 10.5 - 2i

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Find the midpoint
m of
z_(1)=(5-6i) and
z_(2)=(16+2i).
Express your answer in rectangular form.

m=

Find the midpoint $m$ of $z_{1}=(5-6 i)$ and $z_{2}=(16+2 i)$ . $\newline$ Express your answer in rectangular form. $\newline$ $m=$

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Algebra 2

Write equations of sine and cosine functions using properties

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Q. Find the midpoint

m

z_{1}=(5-6 i)

and

z_{2}=(16+2 i)

\newline

Express your answer in rectangular form.

\newline

m=

Formula for finding midpoint: To find the midpoint $m$ of two complex numbers $z_1$ and $z_2$ , we use the formula for the midpoint of two points in the complex plane, which is the average of the real parts and the average of the imaginary parts of the two complex numbers. $\newline$ Let $z_1 = (5 - 6i)$ and $z_2 = (16 + 2i)$ . $\newline$ The real part of the midpoint $m$ is $(\text{Re}(z_1) + \text{Re}(z_2)) / 2$ and the imaginary part of the midpoint $m$ is $(\text{Im}(z_1) + \text{Im}(z_2)) / 2$ .
Given complex numbers: Calculate the real part of the midpoint $m$ : $\text{Re}(m) = \frac{5 + 16}{2} = \frac{21}{2} = 10.5$
Calculate real part of midpoint: Calculate the imaginary part of the midpoint $m$ : $\text{Im}(m) = \frac{-6 + 2}{2} = \frac{-4}{2} = -2$
Calculate imaginary part of midpoint: Combine the real and imaginary parts to express the midpoint $m$ in rectangular form: $\newline$ $m = 10.5 - 2i$