Trigonometric Form of a Complex Number In Exercises 15-22, write the complex number in trigonometric form without using a calculator. 15. Imaginary axis 4 3 2+z=2i + 12 -2-1 Real axis

F2 Plot the complex number and find its absolute value. 11 Plot the complex number on the complex plane to the right. What is the absolute value of this complex number? |11|=☐ (Simplify your answer. Type an exact answer, using radicals as needed.) ㅁ 80 F3 000 000 F4 54 #3 F5 MacBook Air F6 F7 F8 % 5 Λ 6 & 29 7 8*

Multiplication with complex numbers in trigonometric form is accomplished by multiplying absolute values and adding angles. How is division with complex numbers in trigonometric form accomplished? Explain.

(Review of Complex Numbers) The three most important facts to know about complex numbers are that • i² = -1 ⚫ every complex number can be written in the form a + bi, where a and b are real numbers ⚫eit = cos(t) + i sin(t) (this is known as Euler's formula) When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify: a+bi = abic di c+ di c+ di c - di =... You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of the following numbers in the form a + bi, where a and b are real numbers. (c) iii2-i+1 (d) eлi