Complex Numbers (Uppersixth Art Pure Maths)

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Test your knowledge on the properties of the imaginary unit i in pure mathematics!

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Complex Numbers (Uppersixth Art Pure Maths)

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Complex Numbers (Uppersixth Art Pure Maths)


Froggy Jumps Complex Numbers (Uppersixth Art Pure Maths)Versión en línea Test your knowledge on the properties of the imaginary unit i in pure mathematics! por EMMATH 1 What is the value of i squared? a -1 b 1 c 0 2 What is i cubed (i^3)? a i b 1 c -i 3 What is the value of i to the fourth power (i^4)? a -1 b 1 c 0 4 Which of the following is a property of i? a i is an integer b i is a rational number c i is not a real number 5 What is the conjugate of the complex number 3 + 4i? a 3 - 4i b 3 + 4i c -3 + 4i 6 If z = a + bi, what is the conjugate of z? a a - bi b a + bi c -a + bi 7 What is the product of a complex number, z=a+bi and its conjugate? a ab b a^2 + b^2 c a^2 - b^2 8 What is the conjugate of -2 - 3i? a 2 - 3i b -2 + 3i c -2 - 3i 9 If z = 5 + 0i, what is its conjugate? a 0 + 5i b 5 + 0i c -5 + 0i 10 What is the conjugate of the complex number 0 + bi? a 0 + bi b bi c 0 - bi 11 What is the sum of (3 + 4i) and (1 + 2i)? a 2 + 2i b 3 + 5i c 4 + 6i 12 (2 + 7i)-(5 + 3i)= a -3 + 4i b 3 + 10i c 7 + 2i 13 What is the result of (2 + 3i) + (4 - 2i)? a 6 + i b 2 + 5i c 6 + 5i 14 If z1 = 1 + i and z2 = 2 - 3i, what is z1 + z2? a 3 + 2i b 1 - 2i c 3 - 2i 15 What is (7 + 5i) - (3 + 2i)? a 10 + 7i b 4 + 2i c 4 + 3i 16 What is the sum of (0 + 0i) and (0 + 0i)? a 0 + i b 0 + 0i c 0 + 1i 17 When subtracting (a + bi) from (c + di), what is the result? a (c + a) + (d + b)i b (a - c) + (b - d)i c (c - a) + (d - b)i 18 What is the result of (1 + 2i) + (3 + 4i) - (2 + 3i)? a 1 + 2i b 2 + 3i c 3 + 4i 19 If z1 = 3 + 2i and z2 = 1 + 5i, what is z1 - z2? a 2 - 3i b 4 + 3i c 2 + 3i 20 What is the result of multiplying the complex number 3 + 4i by the scalar 2? a 3 + 8i b 5 + 6i c 6 + 8i 21 If z = 1 + 2i, what is 3z? a 1 + 6i b 3 + 2i c 3 + 6i 22 How do you express the multiplication of a complex number by a scalar? a k(a + bi) = ka + kbi b k(a + bi) = a + bi c k(a + bi) = k^2(a + bi) 23 What is the imaginary part of 4(1 + 2i)? a 2 b 4 c 8 24 If k = -1 and z = 3 + 4i, what is kz? a 3 + 4i b -3 - 4i c -3 + 4i 25 If z = 2 - 3i and k = 0, what is kz? a 0 b undefined c 2 - 3i 26 What is the result of multiplying the complex number 0 + 1i by the scalar 5? a 5 + 0i b 1 + 5i c 0 + 5i 27 What is the product of (3 + 4i) and (1 + 2i)? a 7 + 8i b 1 + 10i c -5 + 14i 28 What is the result of (a + bi)(c + di)? a ac + adi + bci + bdi^2 b ac - bd + (ad - bc)i c ac + bd + (ad + bc)i 29 What does i represent in complex numbers? a The real unit, √1 b The zero unit, 0 c The imaginary unit, √-1 30 What is the product of (2 - 3i) and (4 + i)? a 8 - 12i b 11 - 10i c 6 + 5i 31 How do you simplify i^2 in complex multiplication? a i^2 = 0 b i^2 = -1 c i^2 = 1 32 What is the real part of the product (1 + i)(1 - i)? a 2 b 1 c 0 33 If z1 = 2 + 3i and z2 = 4 - i, what is z1 x z2 ? a 8 + 5i b 11 + 10i c 7 + 9i 34 What is the imaginary part of (5 + 2i)(3 + 4i)? a 15 b 26 c 20 35 What happens to the imaginary unit when squared? a It remains i. b It becomes 1. c It becomes -1.

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Complex Numbers (Uppersixth Art Pure Maths)Versión en línea

por EMMATH

What is the value of i squared?

What is i cubed (i^3)?

What is the value of i to the fourth power (i^4)?

Which of the following is a property of i?

What is the conjugate of the complex number 3 + 4i?

If z = a + bi, what is the conjugate of z?

What is the product of a complex number, z=a+bi and its conjugate?

What is the conjugate of -2 - 3i?

If z = 5 + 0i, what is its conjugate?

What is the conjugate of the complex number 0 + bi?

What is the sum of (3 + 4i) and (1 + 2i)?

(2 + 7i)-(5 + 3i)=

What is the result of (2 + 3i) + (4 - 2i)?

If z1 = 1 + i and z2 = 2 - 3i, what is z1 + z2?

What is (7 + 5i) - (3 + 2i)?

What is the sum of (0 + 0i) and (0 + 0i)?

When subtracting (a + bi) from (c + di), what is the result?

What is the result of (1 + 2i) + (3 + 4i) - (2 + 3i)?

If z1 = 3 + 2i and z2 = 1 + 5i, what is z1 - z2?

What is the result of multiplying the complex number 3 + 4i by the scalar 2?

If z = 1 + 2i, what is 3z?

How do you express the multiplication of a complex number by a scalar?

What is the imaginary part of 4(1 + 2i)?

If k = -1 and z = 3 + 4i, what is kz?

If z = 2 - 3i and k = 0, what is kz?

What is the result of multiplying the complex number 0 + 1i by the scalar 5?

What is the product of (3 + 4i) and (1 + 2i)?

What is the result of (a + bi)(c + di)?

What does i represent in complex numbers?

What is the product of (2 - 3i) and (4 + i)?

How do you simplify i^2 in complex multiplication?

What is the real part of the product (1 + i)(1 - i)?

If z1 = 2 + 3i and z2 = 4 - i, what is z1 x z2 ?

What is the imaginary part of (5 + 2i)(3 + 4i)?

What happens to the imaginary unit when squared?