Exercise 5.1 Express each of the complex numbers given in the Exercises 1 to 10 in the form a + ib As (5i)(- 3i/5) just simplifies to 3 which is just a Real…
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1. Evaluate [i18 + (1/i)25]3 Let’s simplify this equation 2. For any two complex numbers z1 and z2, prove that Re(z1 z2) = Re(z1) Re(z2) – Im(z1) Im(z2) Let’s suppose thatz1 = a…
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Solve each of the following equations: 1. x2 + 3 = 0 x2 + 3 = 0 x2 = – 3 x = ± √-3 This can be rewritten as followingx = ±…
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Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2. 1. z = – 1 – i √3 Any Complex Number of form z = a…
Read more14. Express the following expression in the form of a + ib : (3 + i√5)(3 – i√5)/[(√3 + √2i) – (√3 – i√2)] Thus (3 + i√5)(3 – i√5)/[(√3 + √2i) –…
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13. – i Multiplicative Inverse of any Complex Number of form a + ib is equals to 1/a + ib⇒ Multiplicative inverse of – i is equals to 1/- i Thus Multiplicative Inverse…
Read more12. √5 + 3i Multiplicative Inverse of any Complex Number of form a + ib is equals to 1/a + ib⇒ Multiplicative inverse of √5 + 3i is equals to 1/(√5 + 3i)…
Read more11. 4 – 3i Multiplicative Inverse of any Complex Number of form a + ib is equals to 1/a + ib⇒ Multiplicative inverse of 4 – 3i is equals to 1/4 – 3i…
Read more10. (- 2 – 1/3i)3 Thus (- 2 – 1/3i)3 can be written as – 22/3 + 107i/27 in the a + ib form
Read more9. (1/3 + 3i)3 Thus (1/3 + 3i)3 can be written as – 242/9 – 26i in the a + bi form
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