z1=3.45∠980° = 3.45 ∠ 260o
= 3.45(cos 260o + j sin 260o)
= −0.6 − 3.4i
z2=5+9i
=Now,r=(5)2+(9)2=106
And,θ=arctan(59) = 610
z2 = 106 (cos(610)+jsin(610))
(1) z1+z2 in polar form
z1+z2 = (−0.6 − 3.4j) + (5+9j) = 4.4 + 5.6j
In polar form,
Now,r=(4.4)2+(5.6)2=7.12
And,θ=arctan(4.45.60)
Hence, 4.40 + 5.60j = 7.12 ∠ 51.84o [Answer]
(2) z1-z2 trigonometric form
z1- z2 =( −0.6 − 3.4i) - (5+9i)
= -5.6 - 12.4j
In trigonometric form
Now,r=(−5.6)2+(−12.4)2=13.606
And,θ=arctan(−5.6−12.4)
= 2460
Thus,
z1- z2 = 13.606 (cos (2460)+jsin(2460)) [Answer]
(3) z2*z1 exponential form
z1=3.45∠980° = 3.45ej(180980π) = 3.45ej(5.44π)
z2 = 5 +9j = 106ej(18061π)=106ej(0.34π)
hence,
z2*z1 = 3.45ej(5.44π)∗106ej(0.34π)
=3.45∗106ej(5.44π+0.34π))
= 35.52ej(5.78π) [Answer]
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