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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 m of z1=(5−6i) z_{1}=(5-6 i) and z2=(16+2i) z_{2}=(16+2 i) .\newlineExpress your answer in rectangular form.\newlinem= m=

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Q. Find the midpoint m m of z1=(5−6i) z_{1}=(5-6 i) and z2=(16+2i) z_{2}=(16+2 i) .\newlineExpress your answer in rectangular form.\newlinem= m=
  1. Formula for finding midpoint: To find the midpoint mm of two complex numbers z1z_1 and z2z_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.\newlineLet z1=(5−6i)z_1 = (5 - 6i) and z2=(16+2i)z_2 = (16 + 2i).\newlineThe real part of the midpoint mm is (Re(z1)+Re(z2))/2(\text{Re}(z_1) + \text{Re}(z_2)) / 2 and the imaginary part of the midpoint mm is (Im(z1)+Im(z2))/2(\text{Im}(z_1) + \text{Im}(z_2)) / 2.
  2. Given complex numbers: Calculate the real part of the midpoint mm:Re(m)=5+162=212=10.5\text{Re}(m) = \frac{5 + 16}{2} = \frac{21}{2} = 10.5
  3. Calculate real part of midpoint: Calculate the imaginary part of the midpoint mm:Im(m)=−6+22=−42=−2\text{Im}(m) = \frac{-6 + 2}{2} = \frac{-4}{2} = -2
  4. Calculate imaginary part of midpoint: Combine the real and imaginary parts to express the midpoint mm in rectangular form:\newlinem=10.5−2im = 10.5 - 2i

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