Question

Simplify and express your answer in both polar and standard form.
Question 1
(7 cis(45°))²

Q2 below
(-2+2i√3)^5

Answer 1

Simplifying and expressing each term in standard and polar form are respectively; 49/2 and  -512 - 512i√3

How to express an equation in polar form?

1) We are given the expression;

[7 cos (45)]²

We know that cos (45) in standard form is 1/√2. Thus;

[7 cos (45)]² = (7 * 1/√2)² = 49/2

2) We are given the expression;

(-2 + 2i√3)⁵

Using binomial theorem, we have;

(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵

Simplifying each term gives;

−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3

⇒ -512 - 512i√3

Read more about Polar form at; https://brainly.com/question/27844433

#SPJ1