Algebra Answers

Given that z=1+i√z ,express in the form a+ib each of the complex numbers p=z+1/z ,q=z-1/z . In an Argand diagram ,P and Q are the points which represent p and q respectively . O is the origin , M is the midpoint of PQ and G is the point on OM such that OG=two-thirds of OM . Prove that angle PGQ is a right angle . Please I need the answers as soon as possible . Thanks

Find the modulus and the principal argument of each of the given complex numbers. (a) 3 −4i, (b) −2+i, (c) 1 1 +i√ 3 , (d) 7 −i −4−3i, (e) 5(cosπ/3 + isinπ/3), (f) cos2π/3−sin2π/3.

Mart is 4 times the age of his son Matthew. In 8 years, he will be eight-thirds of his son's age. How old is Mart

Find the modulus and the principal argument of each of the given complex numbers. (a) 3 − 4i, (b) −2 + i, (c) 1/1 + i √3 (d) (7 − i)/(-4 - 3i) (e) 5(cos π/3 + isin π/3) (f) cos 2π/3 − sin 2π/3.

12. Use De Moivre's theorem to simplify the following
a. ( cos(-30)+isin(-30))-⁴
b. (Cos20+isin20)-³
c.(cos(-30)+isin(-30))-⁴

13. Express -1+I in polar form. Hence show that(-1+i)¹⁶ is real and that 1/(-+i)⁶ is purely imaginary, giving the value for each

Brian is buying fruit for picnic. He needs at least 100 pieces, but doesnt want more than 110.

The fruit shop sells fruit in bags. Apples come in bags of 10, orange come in bags of 8, passionfruit come in bags of 12 and pears come in bags of 6.

What combination of fruit bags could Brian buy for the party? List some possibilities.

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Find the sum of finite geometric series
: 2+1/2 + 1/4 +1/8 ............+1/2^(n-1)

Express −1 + i in polar form. Hence show that (−1 + i )^16 is real and that 1/(−1 + i )^6
is purely imaginary, giving the value for each.

Simplify the following expressions:
(a) (cos π/4 + i sin π/4)(cos 3π/4 + isin 3π/4)

(b) (cos π/4 + i sin π/4)^2 / (cos π/6 + isin π/6)