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Prove each of the following statements, following the style of the proposition shown below. We may write z as a + bi and w as c + di. Then - (a - bi) + (c - di) by-definition-of-conjugate by-basic algebra by~definition-of-conjugate by-definition-of-complex-addition Hints: for part (f), use part (e). For (g) and (h) see the exercise shown below Exercise 2.2.7. Given that z = a bi is a complex number and z 0 (recall that 0 is the same as 0 + Oi). Show that the complex number a2 +b2 a2 b2 satisfies zw wz- 1, where z a + bi. Hint 2.6 c. If a is real, then az - az Hint 2.6 zl z11-Hint 2.6 izl is a pure imaginary number. z+1

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