Complex Numbers - Page 1 Review

Flashcards covering key complex-number concepts from Page 1: modulus, conjugate, inverse, real/imaginary parts, non-real condition, polynomial expansion, and basic operations.

What is the modulus of 5 + 4i?

sqrt(41)

What is the conjugate of 2 - i?

2 + i

What is the multiplicative inverse of 1 + i?

(1 - i)/2

What is the conjugate of 4 + 3i?

4 - 3i

If z = a + bi with a, b real, what are the real part and imaginary part of z?

Real part = a; Imaginary part = b.

What is a complex number?

A number of the form a + ib where a and b are real numbers.

Expand (z + 3)(z + 3).

z^2 + 6z + 9.

For real x and y, x + iy is non-real when which condition holds?

y ≠ 0.

Sum i + i^2 + i^3 + … up to 1000 terms equals what?

0.

If z1 = a + ib and z2 = c + id with a, b, c, d real, what is z1 + z2?

(a + c) + i(b + d)

What is the conjugate of a + ib?

a - ib